Pair of linear equation s class 10 imp

 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 = 12 × AB × PM

= 12 × 4 × 4 = 8 sq. units.