Mathematics — Standard (041) — CBSE Class 10 board question

For x = 4: This is a vertical line parallel to the y-axis passing through x = 4.

Points: (4, 0), (4, 2), (4, –2)

For 3x – 2y = 6: Rewrite as $y = \dfrac{3x-6}{2}$

| x | 0 | 2 | 4 |
|---|---|---|---|
| y | –3 | 0 | 3 |

Points: (0, –3), (2, 0), (4, 3)

Plot both lines on the graph. The line x = 4 is vertical; the line 3x – 2y = 6 passes through (0, –3) and (2, 0).

The two lines intersect at (4, 3).

∴ Solution: x = 4, y = 3

Source: Chapter 3, Section 3.2 — Graphical Method of Solution of a Pair of Linear Equations

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• Examiners expect a table of values for the non-vertical equation and at least two named points for the vertical line.
• The vertical line x = 4 scores easy marks — just state it is parallel to the y-axis through x = 4.
• Substitute the answer back to verify: 3(4) – 2(3) = 12 – 6 = 6 ✓
• Always state the solution clearly as a coordinate pair at the end — that line carries marks.