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Chapter: Linear Equations in Two Variables· Mathematics Part 1 (Algebra)

Asked in: March 2025 board paper; March 2024 asked the same idea with \(x + y = 4\) (type of triangle with the axes and its area)Draw the graphs representing the equation \(2x = y + 2\) and \(4x + 3y = 24\) on the same graph paper. Find the area of t…

Asked in: March 2025 board paper; March 2024 asked the same idea with \(x + y = 4\) (type of triangle with the axes and its area)

Draw the graphs representing the equation \(2x = y + 2\) and \(4x + 3y = 24\) on the same graph paper. Find the area of the triangle formed by these lines and the X-axis.

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Answer: The lines meet at (3, 4); area of the triangle = 10 sq. units

Line 1: \(2x = y + 2 \Rightarrow y = 2x - 2\)

\(x\)013
\(y\)−204

Line 2: \(4x + 3y = 24\)

\(x\)063
\(y\)804

[Figure: Both lines plotted on the same axes. Line 1 cuts the X-axis at A(1, 0); line 2 cuts the X-axis at B(6, 0); the two lines intersect at P(3, 4). Triangle PAB is shaded.]

Base \(AB = 6 - 1 = 5\) units. Height = distance of P from the X-axis = 4 units.

Area \(= \dfrac{1}{2} \times \text{base} \times \text{height} = \dfrac{1}{2} \times 5 \times 4 = 10\) sq. units.

Doubtly AI · 29 Oct 2026 AI-verified · Nov 2026 Report
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