<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <meta name="aspect-ratio" content="4:3">
  <style>
    * { box-sizing: border-box; margin: 0; padding: 0; }
    body {
      font-family: system-ui, -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, sans-serif;
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      color: #1e2945;
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      flex-direction: column;
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      justify-content: space-between;
      min-height: 100%;
      gap: 12px;
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    .header-badge {
      display: inline-flex;
      align-items: center;
      gap: 6px;
      background: #f1f5f9;
      padding: 6px 14px;
      border-radius: 20px;
      font-size: 15px;
      font-weight: 600;
    }
    .var-x { color: #2563eb; }
    .var-y { color: #d97706; }

    .grid-container {
      display: grid;
      grid-template-columns: 1fr 1fr;
      gap: 12px;
      width: 100%;
      max-width: 540px;
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      .grid-container {
        grid-template-columns: 1fr;
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    }

    .eq-card {
      background: #f8fafc;
      border: 1px solid #e2e8f0;
      border-radius: 12px;
      padding: 12px;
      display: flex;
      flex-direction: column;
      gap: 10px;
    }

    .eq-title {
      font-size: 13px;
      font-weight: 700;
      color: #64748b;
      text-transform: uppercase;
      letter-spacing: 0.5px;
    }

    .step-box {
      background: #ffffff;
      border: 1px solid #e2e8f0;
      border-radius: 8px;
      padding: 8px 10px;
      font-size: 15px;
      font-weight: 600;
      font-family: ui-monospace, SFMono-Regular, Menlo, Monaco, Consolas, monospace;
      transition: opacity 0.3s ease, transform 0.3s ease;
    }

    .step-box.hidden {
      opacity: 0.2;
      transform: translateY(2px);
    }

    .step-arrow {
      text-align: center;
      color: #94a3b8;
      font-size: 12px;
      line-height: 1;
    }

    .verify-box {
      background: #e6f9ed;
      border: 1px solid #b7ebc6;
      color: #137333;
      border-radius: 8px;
      padding: 8px 10px;
      font-size: 15px;
      font-weight: 700;
      display: flex;
      align-items: center;
      justify-content: space-between;
      transition: opacity 0.3s ease, transform 0.3s ease;
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    .verify-box.hidden {
      opacity: 0;
      transform: translateY(4px);
    }

    .checkmark {
      display: inline-flex;
      align-items: center;
      justify-content: center;
      width: 20px;
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      opacity: 0;
      transform: translateY(4px);
    }

    .nav-controls {
      display: flex;
      align-items: center;
      gap: 8px;
    }

    .btn-step {
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      border: 1px solid #cbd5e1;
      color: #334155;
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      font-weight: 600;
      cursor: pointer;
      user-select: none;
    }

    .btn-step.active {
      background: #2563eb;
      border-color: #2563eb;
      color: #ffffff;
    }
  </style>
</head>
<body>

  <div class="header-badge">
    Candidate: (<span class="var-x">x = 7</span>, <span class="var-y">y = 3</span>)
  </div>

  <div class="grid-container">
    
    <div class="eq-card">
      <div class="eq-title">Equation 1</div>
      <div class="step-box" id="eq1-base">
        <span class="var-x">x</span> + <span class="var-y">y</span> = 10
      </div>
      <div class="step-arrow">↓ substitute</div>
      <div class="step-box hidden" id="eq1-sub">
        <span class="var-x">7</span> + <span class="var-y">3</span> = 10
      </div>
      <div class="verify-box hidden" id="eq1-res">
        <span>10 = 10 (True)</span>
        <span class="checkmark">✓</span>
      </div>
    </div>

    
    <div class="eq-card">
      <div class="eq-title">Equation 2</div>
      <div class="step-box" id="eq2-base">
        <span class="var-x">x</span> − <span class="var-y">y</span> = 4
      </div>
      <div class="step-arrow">↓ substitute</div>
      <div class="step-box hidden" id="eq2-sub">
        <span class="var-x">7</span> − <span class="var-y">3</span> = 4
      </div>
      <div class="verify-box hidden" id="eq2-res">
        <span>4 = 4 (True)</span>
        <span class="checkmark">✓</span>
      </div>
    </div>
  </div>

  <div class="solution-banner hidden" id="banner">
    Both true → (7, 3) is a solution!
  </div>

  <div class="nav-controls">
    <button class="btn-step active" id="btn-0" onclick="goToStep(0)">1. System</button>
    <button class="btn-step" id="btn-1" onclick="goToStep(1)">2. Substitute</button>
    <button class="btn-step" id="btn-2" onclick="goToStep(2)">3. Verify</button>
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</body>
</html>

Understanding Systems of Linear Equations

<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <meta name="aspect-ratio" content="1:1">
  <style>
    * { box-sizing: border-box; margin: 0; padding: 0; }
    body {
      font-family: system-ui, -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, sans-serif;
      color: #1e2945;
      background: #ffffff;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: space-between;
      width: 100%;
      height: 100%;
      padding: 10px;
      user-select: none;
    }
    .controls {
      display: flex;
      gap: 6px;
      flex-wrap: wrap;
      justify-content: center;
      width: 100%;
      margin-bottom: 6px;
    }
    .btn {
      padding: 5px 10px;
      font-size: 13px;
      font-weight: 600;
      border-radius: 6px;
      border: 1px solid #e2e8f0;
      background: #f8fafc;
      color: #64748b;
      cursor: pointer;
      transition: all 0.2s ease;
    }
    .btn.active {
      background: #0ea5e9;
      color: #ffffff;
      border-color: #0ea5e9;
      box-shadow: 0 2px 6px rgba(14, 165, 233, 0.3);
    }
    .btn-a.active {
      background: #2563eb;
      border-color: #2563eb;
      box-shadow: 0 2px 6px rgba(37, 99, 235, 0.3);
    }
    .btn-b.active {
      background: #ea580c;
      border-color: #ea580c;
      box-shadow: 0 2px 6px rgba(234, 88, 12, 0.3);
    }
    .btn-sol.active {
      background: #10b981;
      border-color: #10b981;
      box-shadow: 0 2px 6px rgba(16, 185, 129, 0.3);
    }
    .svg-container {
      width: 100%;
      max-width: 420px;
      flex: 1;
      display: flex;
      align-items: center;
      justify-content: center;
    }
    svg {
      width: 100%;
      height: 100%;
      overflow: visible;
    }
    .grid-line {
      stroke: #f1f5f9;
      stroke-width: 1;
    }
    .axis-line {
      stroke: #64748b;
      stroke-width: 1.5;
    }
    .axis-label {
      font-size: 11px;
      fill: #94a3b8;
      font-weight: 500;
      text-anchor: middle;
      dominant-baseline: middle;
    }
    .line-a {
      stroke: #2563eb;
      stroke-width: 3;
      stroke-linecap: round;
      transition: opacity 0.3s ease, stroke-width 0.3s ease;
    }
    .line-b {
      stroke: #ea580c;
      stroke-width: 3;
      stroke-linecap: round;
      transition: opacity 0.3s ease, stroke-width 0.3s ease;
    }
    .line-dim {
      opacity: 0.2;
    }
    .line-focus {
      stroke-width: 4.5;
    }
    .callout-bg {
      fill: #ffffff;
      stroke: #10b981;
      stroke-width: 1.5;
      filter: drop-shadow(0 2px 5px rgba(0,0,0,0.08));
    }
    .pulse-ring {
      animation: pulse 2s infinite ease-out;
      transform-origin: 238px 275px;
    }
    @keyframes pulse {
      0% { r: 6; opacity: 0.8; }
      100% { r: 18; opacity: 0; }
    }
  </style>
</head>
<body>

  <div class="controls">
    <button class="btn active" id="btnAll" onclick="setMode('all')">Both Lines</button>
    <button class="btn btn-a" id="btnA" onclick="setMode('a')">y = −x + 10</button>
    <button class="btn btn-b" id="btnB" onclick="setMode('b')">y = x − 4</button>
    <button class="btn btn-sol" id="btnSol" onclick="setMode('sol')">Intersection (7, 3)</button>
  </div>

  <div class="svg-container">
    <svg viewBox="0 0 400 400">
      <defs>
        
        <marker id="arrow" viewBox="0 0 6 6" refX="4" refY="3" markerWidth="4" markerHeight="4" orient="auto-start-reverse">
          <path d="M 0 0 L 6 3 L 0 6 z" fill="#64748b"/>
        </marker>
      </defs>

      
      
      
      <g id="grid">
        
        <line x1="40" y1="20" x2="40" y2="360" class="grid-line" />
        <line x1="96.67" y1="20" x2="96.67" y2="360" class="grid-line" />
        <line x1="153.33" y1="20" x2="153.33" y2="360" class="grid-line" />
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        <line x1="40" y1="190" x2="380" y2="190" class="grid-line" />
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      <text x="392" y="375" class="axis-label" style="font-weight:700; fill:#1e2945;">x</text>
      <text x="25" y="10" class="axis-label" style="font-weight:700; fill:#1e2945;">y</text>

      
      <text x="40" y="375" class="axis-label">0</text>
      <text x="96.67" y="375" class="axis-label">2</text>
      <text x="153.33" y="375" class="axis-label">4</text>
      <text x="210" y="375" class="axis-label">6</text>
      <text x="266.67" y="375" class="axis-label">8</text>
      <text x="323.33" y="375" class="axis-label">10</text>
      <text x="380" y="375" class="axis-label">12</text>

      <text x="25" y="303.33" class="axis-label">2</text>
      <text x="25" y="246.67" class="axis-label">4</text>
      <text x="25" y="190" class="axis-label">6</text>
      <text x="25" y="133.33" class="axis-label">8</text>
      <text x="25" y="76.67" class="axis-label">10</text>
      <text x="25" y="20" class="axis-label">12</text>

      
      
      <line id="lineA" x1="40" y1="76.67" x2="337.5" y2="374.17" class="line-a" />

      
      
      <line id="lineB" x1="139.17" y1="374.17" x2="380" y2="133.33" class="line-b" />

      
      <g id="lblA" transform="translate(68, 62)">
        <rect x="0" y="0" width="80" height="20" rx="4" fill="#eff6ff" stroke="#bfdbfe" stroke-width="1"/>
        <text x="40" y="13" font-size="11" font-weight="700" fill="#2563eb" text-anchor="middle">y = −x + 10</text>
      </g>

      <g id="lblB" transform="translate(295, 172)">
        <rect x="0" y="0" width="70" height="20" rx="4" fill="#fff7ed" stroke="#fed7aa" stroke-width="1"/>
        <text x="35" y="13" font-size="11" font-weight="700" fill="#ea580c" text-anchor="middle">y = x − 4</text>
      </g>

      
      <g id="groupSol">
        
        <polyline points="238.33,275 275,230 355,230" fill="none" stroke="#10b981" stroke-width="1.5" stroke-dasharray="3,3" />

        
        <rect x="230" y="178" width="160" height="42" rx="8" class="callout-bg" />
        <text x="310" y="196" font-size="12" font-weight="800" fill="#047857" text-anchor="middle">Solution: (7, 3)</text>
        <text x="310" y="211" font-size="10" font-weight="600" fill="#64748b" text-anchor="middle">Solves both equations</text>

        
        <circle cx="238.33" cy="275" r="8" fill="#10b981" class="pulse-ring" />
        <circle cx="238.33" cy="275" r="5" fill="#10b981" stroke="#ffffff" stroke-width="2" />
      </g>

    </svg>
  </div>

  <script>
    function setMode(mode) {
      const btnAll = document.getElementById('btnAll');
      const btnA = document.getElementById('btnA');
      const btnB = document.getElementById('btnB');
      const btnSol = document.getElementById('btnSol');

      const lineA = document.getElementById('lineA');
      const lineB = document.getElementById('lineB');
      const lblA = document.getElementById('lblA');
      const lblB = document.getElementById('lblB');
      const groupSol = document.getElementById('groupSol');

      [btnAll, btnA, btnB, btnSol].forEach(b => b.classList.remove('active'));

      if (mode === 'all') {
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        lineA.className.baseVal = 'line-a';
        lineB.className.baseVal = 'line-b';
        lblA.style.opacity = '1';
        lblB.style.opacity = '1';
        groupSol.style.opacity = '1';
      } else if (mode === 'a') {
        btnA.classList.add('active');
        lineA.className.baseVal = 'line-a line-focus';
        lineB.className.baseVal = 'line-b line-dim';
        lblA.style.opacity = '1';
        lblB.style.opacity = '0.3';
        groupSol.style.opacity = '0.2';
      } else if (mode === 'b') {
        btnB.classList.add('active');
        lineA.className.baseVal = 'line-a line-dim';
        lineB.className.baseVal = 'line-b line-focus';
        lblA.style.opacity = '0.3';
        lblB.style.opacity = '1';
        groupSol.style.opacity = '0.2';
      } else if (mode === 'sol') {
        btnSol.classList.add('active');
        lineA.className.baseVal = 'line-a';
        lineB.className.baseVal = 'line-b';
        lblA.style.opacity = '0.6';
        lblB.style.opacity = '0.6';
        groupSol.style.opacity = '1';
      }
    }
  </script>
</body>
</html>

<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <meta name="aspect-ratio" content="4:3">
  <title>Testing Solutions in a Linear System</title>
  <style>
    * {
      box-sizing: border-box;
      margin: 0;
      padding: 0;
    }
    body {
      font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Helvetica, Arial, sans-serif;
      background: #ffffff;
      color: #1e293b;
      padding: 12px;
      line-height: 1.4;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: center;
      min-height: 100%;
    }
    .wrapper {
      width: 100%;
      max-width: 620px;
      display: flex;
      flex-direction: column;
      gap: 12px;
    }
    /* Candidate Selector Tabs */
    .controls {
      display: flex;
      justify-content: center;
      gap: 8px;
      flex-wrap: wrap;
    }
    .pill-btn {
      background: #f1f5f9;
      border: 1.5px solid #cbd5e1;
      border-radius: 9999px;
      padding: 6px 14px;
      font-size: 13px;
      font-weight: 600;
      color: #475569;
      cursor: pointer;
      display: inline-flex;
      align-items: center;
      gap: 6px;
      transition: all 0.2s ease;
    }
    .pill-btn:hover {
      background: #e2e8f0;
      border-color: #94a3b8;
    }
    .pill-btn.active {
      background: #e0e7ff;
      border-color: #6366f1;
      color: #3730a3;
      box-shadow: 0 1px 3px rgba(99, 102, 241, 0.2);
    }
    .var-x {
      color: #2563eb;
      font-weight: 700;
    }
    .var-y {
      color: #7c3aed;
      font-weight: 700;
    }

    /* Grid of Equations */
    .grid-duo {
      display: grid;
      grid-template-columns: 1fr 1fr;
      gap: 12px;
    }
    @media (max-width: 500px) {
      .grid-duo {
        grid-template-columns: 1fr;
      }
    }

    /* Verification Cards */
    .eq-card {
      border-radius: 14px;
      padding: 14px;
      display: flex;
      flex-direction: column;
      gap: 10px;
      transition: background 0.25s ease, border-color 0.25s ease;
    }
    .eq-card.pass {
      background: #f0fdf4;
      border: 1.5px solid #a7f3d0;
    }
    .eq-card.fail {
      background: #fff1f2;
      border: 1.5px solid #fecdd3;
    }

    .card-head {
      display: flex;
      justify-content: space-between;
      align-items: center;
    }
    .tag {
      font-size: 11px;
      font-weight: 700;
      letter-spacing: 0.05em;
      text-transform: uppercase;
    }
    .tag.pass { color: #047857; }
    .tag.fail { color: #be123c; }

    .status-badge {
      font-size: 11px;
      font-weight: 700;
      padding: 2px 8px;
      border-radius: 9999px;
      display: inline-flex;
      align-items: center;
      gap: 4px;
    }
    .status-badge.pass {
      background: #dcfce7;
      color: #15803d;
    }
    .status-badge.fail {
      background: #ffe4e6;
      color: #b91c1c;
    }

    /* Equation Steps */
    .steps-box {
      background: #ffffff;
      border-radius: 10px;
      padding: 10px 12px;
      border: 1px solid rgba(0,0,0,0.06);
      display: flex;
      flex-direction: column;
      gap: 6px;
      font-family: ui-monospace, SFMono-Regular, Menlo, Monaco, Consolas, monospace;
      font-size: 13.5px;
      font-variant-numeric: tabular-nums;
    }
    .step-line {
      display: flex;
      align-items: center;
      justify-content: space-between;
    }
    .step-label {
      font-size: 10px;
      color: #94a3b8;
      font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, sans-serif;
      text-transform: uppercase;
      font-weight: 600;
    }
    .step-val {
      color: #1e293b;
      font-weight: 600;
    }
    .step-val.eval-pass {
      color: #059669;
      font-weight: 700;
    }
    .step-val.eval-fail {
      color: #e11d48;
      font-weight: 700;
    }

    /* Bottom Verdict Banner */
    .banner {
      border-radius: 12px;
      padding: 12px 14px;
      display: flex;
      align-items: center;
      justify-content: space-between;
      gap: 12px;
      transition: all 0.25s ease;
    }
    .banner.fail {
      background: #fff1f2;
      border: 1.5px solid #fda4af;
      color: #881337;
    }
    .banner.pass {
      background: #f0fdf4;
      border: 1.5px solid #86efac;
      color: #064e3b;
    }

    .banner-text-group {
      display: flex;
      align-items: center;
      gap: 10px;
      font-size: 12.5px;
      font-weight: 500;
    }
    .banner-icon {
      font-size: 18px;
      line-height: 1;
      flex-shrink: 0;
    }
    .verdict-pill {
      font-size: 12px;
      font-weight: 700;
      padding: 6px 12px;
      border-radius: 8px;
      white-space: nowrap;
      flex-shrink: 0;
      color: #ffffff;
      box-shadow: 0 1px 2px rgba(0,0,0,0.1);
    }
    .verdict-pill.fail { background: #e11d48; }
    .verdict-pill.pass { background: #059669; }
  </style>
</head>
<body>

  <div class="wrapper">
    
    <div class="controls">
      <button class="pill-btn active" onclick="setCandidate(0)" id="btn-0">
        Test Point <strong>(<span class="var-x">8</span>, <span class="var-y">2</span>)</strong>
      </button>
      <button class="pill-btn" onclick="setCandidate(1)" id="btn-1">
        Test Point <strong>(<span class="var-x">7</span>, <span class="var-y">3</span>)</strong>
      </button>
      <button class="pill-btn" onclick="setCandidate(2)" id="btn-2">
        Test Point <strong>(<span class="var-x">5</span>, <span class="var-y">1</span>)</strong>
      </button>
    </div>

    
    <div class="grid-duo">
      
      <div class="eq-card pass" id="card-1">
        <div class="card-head">
          <span class="tag pass" id="tag-1">Equation 1</span>
          <span class="status-badge pass" id="badge-1">✓ TRUE</span>
        </div>
        <div class="steps-box">
          <div class="step-line">
            <span class="step-label">Equation</span>
            <span class="step-val">x + y = 10</span>
          </div>
          <div class="step-line">
            <span class="step-label">Substitute</span>
            <span class="step-val" id="sub-1">(<span class="var-x">8</span>) + (<span class="var-y">2</span>) = 10</span>
          </div>
          <div class="step-line">
            <span class="step-label">Evaluate</span>
            <span class="step-val eval-pass" id="eval-1">10 = 10</span>
          </div>
        </div>
      </div>

      
      <div class="eq-card fail" id="card-2">
        <div class="card-head">
          <span class="tag fail" id="tag-2">Equation 2</span>
          <span class="status-badge fail" id="badge-2">✕ FALSE</span>
        </div>
        <div class="steps-box">
          <div class="step-line">
            <span class="step-label">Equation</span>
            <span class="step-val">x − y = 4</span>
          </div>
          <div class="step-line">
            <span class="step-label">Substitute</span>
            <span class="step-val" id="sub-2">(<span class="var-x">8</span>) − (<span class="var-y">2</span>) = 4</span>
          </div>
          <div class="step-line">
            <span class="step-label">Evaluate</span>
            <span class="step-val eval-fail" id="eval-2">6 ≠ 4</span>
          </div>
        </div>
      </div>
    </div>

    
    <div class="banner fail" id="banner">
      <div class="banner-text-group">
        <span class="banner-icon" id="banner-icon">⚠</span>
        <span id="banner-msg">A solution must satisfy <strong>both</strong> equations. Because (8, 2) fails Equation 2, it is not a system solution.</span>
      </div>
      <div class="verdict-pill fail" id="verdict-pill">Not a Solution</div>
    </div>
  </div>

  <script>
    const candidates = [
      {
        x: 8,
        y: 2,
        eq1_sub: '(<span class="var-x">8</span>) + (<span class="var-y">2</span>) = 10',
        eq1_eval: '10 = 10',
        eq1_pass: true,
        eq2_sub: '(<span class="var-x">8</span>) − (<span class="var-y">2</span>) = 4',
        eq2_eval: '6 ≠ 4',
        eq2_pass: false,
        msg: 'A solution must satisfy <strong>both</strong> equations. Because (8, 2) fails Equation 2, it is not a system solution.',
        verdict: 'Not a Solution'
      },
      {
        x: 7,
        y: 3,
        eq1_sub: '(<span class="var-x">7</span>) + (<span class="var-y">3</span>) = 10',
        eq1_eval: '10 = 10',
        eq1_pass: true,
        eq2_sub: '(<span class="var-x">7</span>) − (<span class="var-y">3</span>) = 4',
        eq2_eval: '4 = 4',
        eq2_pass: true,
        msg: 'Point (7, 3) satisfies <strong>both</strong> equations simultaneously. It is the solution to the system!',
        verdict: '✓ System Solution'
      },
      {
        x: 5,
        y: 1,
        eq1_sub: '(<span class="var-x">5</span>) + (<span class="var-y">1</span>) = 10',
        eq1_eval: '6 ≠ 10',
        eq1_pass: false,
        eq2_sub: '(<span class="var-x">5</span>) − (<span class="var-y">1</span>) = 4',
        eq2_eval: '4 = 4',
        eq2_pass: true,
        msg: 'Point (5, 1) satisfies Equation 2 but fails Equation 1, so it is not a system solution.',
        verdict: 'Not a Solution'
      }
    ];

    function setCandidate(index) {
      const data = candidates[index];

      // Update button highlights
      for (let i = 0; i < candidates.length; i++) {
        document.getElementById(`btn-${i}`).classList.toggle('active', i === index);
      }

      // Update Card 1
      const c1 = document.getElementById('card-1');
      const tag1 = document.getElementById('tag-1');
      const badge1 = document.getElementById('badge-1');
      const sub1 = document.getElementById('sub-1');
      const eval1 = document.getElementById('eval-1');

      c1.className = `eq-card ${data.eq1_pass ? 'pass' : 'fail'}`;
      tag1.className = `tag ${data.eq1_pass ? 'pass' : 'fail'}`;
      badge1.className = `status-badge ${data.eq1_pass ? 'pass' : 'fail'}`;
      badge1.textContent = data.eq1_pass ? '✓ TRUE' : '✕ FALSE';
      sub1.innerHTML = data.eq1_sub;
      eval1.textContent = data.eq1_eval;
      eval1.className = `step-val ${data.eq1_pass ? 'eval-pass' : 'eval-fail'}`;

      // Update Card 2
      const c2 = document.getElementById('card-2');
      const tag2 = document.getElementById('tag-2');
      const badge2 = document.getElementById('badge-2');
      const sub2 = document.getElementById('sub-2');
      const eval2 = document.getElementById('eval-2');

      c2.className = `eq-card ${data.eq2_pass ? 'pass' : 'fail'}`;
      tag2.className = `tag ${data.eq2_pass ? 'pass' : 'fail'}`;
      badge2.className = `status-badge ${data.eq2_pass ? 'pass' : 'fail'}`;
      badge2.textContent = data.eq2_pass ? '✓ TRUE' : '✕ FALSE';
      sub2.innerHTML = data.eq2_sub;
      eval2.textContent = data.eq2_eval;
      eval2.className = `step-val ${data.eq2_pass ? 'eval-pass' : 'eval-fail'}`;

      // Update Banner
      const isSystemSol = data.eq1_pass && data.eq2_pass;
      const banner = document.getElementById('banner');
      const bannerIcon = document.getElementById('banner-icon');
      const bannerMsg = document.getElementById('banner-msg');
      const verdictPill = document.getElementById('verdict-pill');

      banner.className = `banner ${isSystemSol ? 'pass' : 'fail'}`;
      bannerIcon.textContent = isSystemSol ? '★' : '⚠';
      bannerMsg.innerHTML = data.msg;
      verdictPill.className = `verdict-pill ${isSystemSol ? 'pass' : 'fail'}`;
      verdictPill.textContent = data.verdict;
    }
  </script>
</body>
</html>

<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <title>System of Linear Equations</title>
  <style>
    * {
      box-sizing: border-box;
      margin: 0;
      padding: 0;
    }

    body {
      font-family: system-ui, -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, sans-serif;
      color: #1e2945;
      background: transparent;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: center;
      min-height: 100vh;
      padding: 12px 8px;
      user-select: none;
    }

    .main-wrapper {
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: center;
      width: 100%;
      max-width: 520px;
    }

    .system-container {
      display: flex;
      flex-direction: row;
      align-items: center;
      justify-content: center;
      gap: 6px;
      width: 100%;
    }

    /* Curly brace and equations always stay grouped horizontally */
    .system-core {
      display: flex;
      flex-direction: row;
      align-items: center;
      gap: 6px;
      flex-shrink: 0;
    }

    .brace-wrapper {
      display: flex;
      align-items: center;
      justify-content: center;
      height: 96px;
      flex-shrink: 0;
    }

    .brace-svg {
      width: 18px;
      height: 96px;
      stroke: #1e2945;
      stroke-width: 2.2;
      fill: none;
      stroke-linecap: round;
      stroke-linejoin: round;
    }

    /* Equations Column */
    .equations-column {
      display: flex;
      flex-direction: column;
      gap: 10px;
    }

    .equation-row {
      display: flex;
      align-items: center;
      gap: 8px;
      padding: 4px 8px;
      border-radius: 8px;
      background: rgba(248, 250, 252, 0.7);
      border: 1px solid #e6e6e6;
      transition: background-color 0.2s ease, border-color 0.2s ease;
    }

    .equation-row:hover {
      background: #f1f5f9;
      border-color: #cbd5e1;
    }

    .badge-clue {
      font-size: 11px;
      font-weight: 700;
      text-transform: uppercase;
      letter-spacing: 0.4px;
      padding: 3px 6px;
      border-radius: 5px;
      border: 1px solid #e2e8f0;
      background: #ffffff;
      color: #64748b;
      white-space: nowrap;
    }

    .math-text {
      font-family: "Cambria Math", "STIX Two Math", "Times New Roman", serif;
      font-size: 22px;
      font-weight: 500;
      letter-spacing: 0.5px;
      display: flex;
      align-items: center;
      gap: 3px;
      white-space: nowrap;
    }

    .var-x {
      color: #0284c7;
      font-weight: 700;
      font-style: italic;
      padding: 1px 4px;
      border-radius: 4px;
      transition: background-color 0.2s, outline 0.2s;
      cursor: pointer;
    }

    .var-y {
      color: #d97706;
      font-weight: 700;
      font-style: italic;
      padding: 1px 4px;
      border-radius: 4px;
      transition: background-color 0.2s, outline 0.2s;
      cursor: pointer;
    }

    .highlighted {
      background: rgba(2, 132, 199, 0.18);
      outline: 1.5px solid rgba(2, 132, 199, 0.45);
    }

    .highlighted-y {
      background: rgba(217, 119, 6, 0.18);
      outline: 1.5px solid rgba(217, 119, 6, 0.45);
    }

    /* Pointer & Callout Section */
    .callout-section {
      display: flex;
      flex-direction: row;
      align-items: center;
      flex-shrink: 1;
      min-width: 0;
    }

    .pointer-svg {
      width: 28px;
      height: 96px;
      flex-shrink: 0;
      overflow: visible;
    }

    .pointer-line {
      stroke: #94a3b8;
      stroke-width: 1.5;
      stroke-dasharray: 3 3;
      fill: none;
    }

    .callout-badge {
      display: flex;
      flex-direction: column;
      align-items: flex-start;
      gap: 2px;
      background: #f8fafc;
      border: 1px solid #e6e6e6;
      padding: 8px 10px;
      border-radius: 8px;
      box-shadow: 0 1px 4px rgba(0, 0, 0, 0.04);
      flex-shrink: 1;
    }

    .callout-title {
      font-size: 12px;
      font-weight: 700;
      color: #1e2945;
      white-space: nowrap;
    }

    .callout-vars {
      font-size: 13px;
      font-family: "Cambria Math", serif;
      font-weight: 600;
      white-space: nowrap;
    }

    .sub-hint {
      margin-top: 18px;
      font-size: 12px;
      font-weight: 500;
      color: #64748b;
      display: flex;
      align-items: center;
      gap: 6px;
      text-align: center;
      padding: 0 8px;
    }

    /* Adaptive sizing for wider viewports */
    @media (min-width: 480px) {
      .system-container {
        gap: 10px;
      }
      .system-core {
        gap: 10px;
      }
      .brace-wrapper {
        height: 108px;
      }
      .brace-svg {
        width: 22px;
        height: 108px;
      }
      .equations-column {
        gap: 14px;
      }
      .equation-row {
        padding: 6px 12px;
        gap: 10px;
      }
      .badge-clue {
        font-size: 12px;
        padding: 4px 8px;
      }
      .math-text {
        font-size: 26px;
        gap: 4px;
      }
      .pointer-svg {
        width: 38px;
        height: 108px;
      }
      .callout-badge {
        padding: 10px 14px;
      }
      .callout-title {
        font-size: 13px;
      }
      .callout-vars {
        font-size: 15px;
      }
      .sub-hint {
        font-size: 13px;
        margin-top: 22px;
      }
    }
  </style>
</head>
<body>

  <div class="main-wrapper">
    <div class="system-container">
      
      <div class="system-core">
        
        <div class="brace-wrapper">
          <svg class="brace-svg" viewBox="0 0 20 100" preserveAspectRatio="none">
            <path d="M 18 3 C 6 3, 6 25, 6 44 C 6 48, 2 49, 0.5 50 C 2 51, 6 52, 6 56 C 6 75, 6 97, 18 97" />
          </svg>
        </div>

        
        <div class="equations-column">
          
          <div class="equation-row">
            <span class="badge-clue">Clue 1</span>
            <div class="math-text">
              <span class="var-x" id="x1" title="Click to highlight variable x">x</span>
              <span>+</span>
              <span class="var-y" id="y1" title="Click to highlight variable y">y</span>
              <span>=</span>
              <span>10</span>
            </div>
          </div>

          
          <div class="equation-row">
            <span class="badge-clue">Clue 2</span>
            <div class="math-text">
              <span class="var-x" id="x2" title="Click to highlight variable x">x</span>
              <span>−</span>
              <span class="var-y" id="y2" title="Click to highlight variable y">y</span>
              <span>=</span>
              <span>4</span>
            </div>
          </div>
        </div>
      </div>

      
      <div class="callout-section">
        <svg class="pointer-svg" viewBox="0 0 38 100" preserveAspectRatio="none">
          
          <path class="pointer-line" d="M 0 24 C 20 24, 18 50, 38 50" />
          
          <path class="pointer-line" d="M 0 76 C 20 76, 18 50, 38 50" />
          <circle cx="2" cy="24" r="2.8" fill="#0284c7" />
          <circle cx="2" cy="76" r="2.8" fill="#d97706" />
        </svg>

        
        <div class="callout-badge">
          <span class="callout-title">Shared Variables</span>
          <span class="callout-vars">
            (<span style="color:#0284c7; font-style:italic; font-weight:700;">x</span>, <span style="color:#d97706; font-style:italic; font-weight:700;">y</span>)
          </span>
        </div>
      </div>
    </div>

    
    <div class="sub-hint">
      <span>✦ The same pair (x, y) satisfies both equations simultaneously</span>
    </div>
  </div>

  <script>
    const xs = [document.getElementById('x1'), document.getElementById('x2')];
    const ys = [document.getElementById('y1'), document.getElementById('y2')];

    function setupHighlight(elements, className) {
      let isLocked = false;

      elements.forEach(el => {
        el.addEventListener('mouseenter', () => {
          if (!isLocked) {
            elements.forEach(e => e.classList.add(className));
          }
        });

        el.addEventListener('mouseleave', () => {
          if (!isLocked) {
            elements.forEach(e => e.classList.remove(className));
          }
        });

        el.addEventListener('click', () => {
          isLocked = !isLocked;
          elements.forEach(e => e.classList.toggle(className, isLocked));
        });
      });
    }

    setupHighlight(xs, 'highlighted');
    setupHighlight(ys, 'highlighted-y');
  </script>
</body>
</html>

HSA.REI.C.6

Aligned learning resources

Related diagrams