Question 1. Draw the graph of 2x + y = 6 and 2x – y + 2 = 0. Shade the region bounded by these lines and x-axis. Find the area of the shaded region. [CBSE 2007] Solution: The given system of equation is 2x + y – 6 = 0 ………. (i) 2x – y + 2 = 0 ……… (ii) solutions for each equation of the system are: (i) ⇒ y = 6 – 2x Table of solutions for 2x + y – 6 = 0 Similarly Table of solutions for 2x – y + 2 = 0 Plotting these on the graph These intersect at (1, 4), so this is the solution. In graph, area bounded by the lines and x-axis is ∆PAB which is shaded. Draw PM ⊥ x-axis PM = y-coordinate of P (1, 4) = 4 units and AB = 1 + 3 = 4 units ∴ Area of shaded region = Area of ∆PAB = 1 2 × AB × PM = 1 2 × 4 × 4 = 8 sq. units.
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