Solve the following system of linear equations graphically :
$$x - y + 1 = 0$$
$$x + y = 5$$
Generated by claude-sonnet-4-6 · 2026-06-15 10:33 · grounding rag
Model Answer
For $x - y + 1 = 0$, i.e., $y = x + 1$:
| $x$ | 0 | 2 |
|-----|---|---|
| $y$ | 1 | 3 |
For $x + y = 5$, i.e., $y = 5 - x$:
| $x$ | 0 | 3 |
|-----|---|---|
| $y$ | 5 | 2 |
Plot points A(0, 1), B(2, 3) and P(0, 5), Q(3, 2) on graph paper and draw lines through them.
The two lines intersect at the point (2, 3).
∴ x = 2, y = 3 is the solution.
Verification: $2 - 3 + 1 = 0$ ✓ and $2 + 3 = 5$ ✓
Source: Chapter 3, Section 3.2 – Graphical Method of Solution of a Pair of Linear Equations
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Explanation
- Examiners expect: a table of values for each equation (2 points each), a mention of plotting and drawing lines, the intersection point clearly stated, and a verification step.
- Award breakup (typical): 1 mark for correct tables/graph, 1 mark for correct intersection point, 1 mark for verification.
- Always check your answer by substituting back into both equations — examiners specifically look for this.
- Keep tables neat; two points per line are sufficient for a straight-line graph.