Compute the area bounded by the lines x + 2y = 2, y – x = 1 and 2x + y = 7.

Given;

The lines x + 2y = 2

x = 2 – 2y …. (1)

y – x = 1

⇒ x = y - 1 …. (2)

and 2x + y = 7 …. (3)

Equate the values of x from 1 and 2 to get,

2 – 2y = y – 1

2+1 = y + 2y

3 = 3y

y = 1

put the value of y in (2) to get,

x = 1 -1

= 0

So, intersection point is (0,1).

By solving these equations, we get the points of intersection as (0,1), (2,3) and (4,-1).

Area of the region bounded by the curve y=f(x), the x-axis and the ordinates x=a and x=b, where f(x) is a continuous function defined on [a,b], is given by .

Required area

=3 + (24 − 12) − (12 − 3) = 6 sq.units