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Pair of Linear Equations in Two Variables
CBSE 2026 Board Exam Set 3 (Code 30/1/3)
CBSE_BOARD_PYQ_2026_30_1_3
Grade 10

Question:

[Section D]

Solve the following pair of linear equations graphically:
$x - y + 1 = 0$ and $3x + 2y - 12 = 0$.
Find the coordinates of the vertices of the triangle formed by these lines and the $x$-axis.

Step-by-Step Solution

Key Concept: Plot lines, find intersection point $(2, 3)$, and $x$-intercepts $(-1, 0)$ and $(4, 0)$.
Line 1: $x - y + 1 = 0 \Rightarrow (0, 1), (-1, 0), (2, 3)$.
Line 2: $3x + 2y - 12 = 0 \Rightarrow (0, 6), (4, 0), (2, 3)$.
Intersection point: $(2, 3)$. $x$-intercepts: $(-1, 0)$ and $(4, 0)$.
Vertices of the triangle: $(2, 3)$, $(-1, 0)$, $(4, 0)$. [5.0 Marks]

Correct Answer: Vertices: (2, 3), (-1, 0), (4, 0)
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