Solve the linear equations $3x + y = 14$ and $y = 2$ graphically.
Generated by claude-sonnet-4-6 · 2026-06-15 10:32 · grounding rag
Model Answer
Equation 1: $3x + y = 14$
Find points:
| $x$ | 0 | 2 | 4 |
|-----|---|---|---|
| $y$ | 14 | 8 | 2 |
Equation 2: $y = 2$ (a horizontal line parallel to the x-axis)
| $x$ | 0 | 2 | 4 |
|-----|---|---|---|
| $y$ | 2 | 2 | 2 |
Graph: Plot both lines on the same graph. The line $3x + y = 14$ is a slant line; $y = 2$ is horizontal.
Point of intersection: The two lines meet at (4, 2).
$$\therefore x = 4,\quad y = 2$$
Verification: $3(4) + 2 = 12 + 2 = 14$ ✓
Source: Chapter 3, Exercise 3.1 (Graphical method)
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Explanation
- Examiners expect a table of at least 2–3 points for each line, followed by a note about plotting and the intersection point.
- $y = 2$ is always a horizontal line — all y-values in its table must be 2.
- The point where the two lines cross gives the solution; always verify by substituting back.
- Marks are typically split: 1 mark for correct tables/plotting, 1 mark for identifying the intersection, 1 mark for stating and verifying the solution.