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Pair of Linear Equations in Two Variables
CBSE 2026 Board Exam Set 1 (Code 30/7/1)
CBSE_BOARD_PYQ_2026_30_7_1
Grade 10
Question:
[Section D]
Solve the following system of linear equations graphically:
$$2x - y = 1$$
$$3x + 2y = 12$$
Also, find the coordinates of the vertices of the triangle formed by these lines and the $x$-axis, and calculate its area.
Solve the following system of linear equations graphically:
$$2x - y = 1$$
$$3x + 2y = 12$$
Also, find the coordinates of the vertices of the triangle formed by these lines and the $x$-axis, and calculate its area.
Step-by-Step Solution
Key Concept: Plot lines, intersection point $(2, 3)$, $x$-intercepts at $(0.5, 0)$ and $(4, 0)$. Base $= 3.5$, Height $= 3$.
Table of values for $2x - y = 1$ and $3x + 2y = 12$. [1.0 Mark]
Plotting lines & identifying intersection point $B(2, 3)$. [1.5 Marks]
Vertices of triangle formed with $x$-axis: $A(0.5, 0)$, $B(2, 3)$, $C(4, 0)$. [1.5 Marks]
$\text{Area} = \dfrac{1}{2} \times \text{base} \times \text{height} = \dfrac{1}{2} \times 3.5 \times 3 = 5.25$ sq units. [1.0 Mark]
Plotting lines & identifying intersection point $B(2, 3)$. [1.5 Marks]
Vertices of triangle formed with $x$-axis: $A(0.5, 0)$, $B(2, 3)$, $C(4, 0)$. [1.5 Marks]
$\text{Area} = \dfrac{1}{2} \times \text{base} \times \text{height} = \dfrac{1}{2} \times 3.5 \times 3 = 5.25$ sq units. [1.0 Mark]
Correct Answer: Vertices $(0.5, 0), (2, 3), (4, 0)$, Area $= 5.25$ sq units
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