An important and conceptual question from linear equations in two variables in which we have to solve the equations graphically and also asked to find the vertices and the area of the triangle formed by these lines and the x-axis if the equations are x-2y+2=0, 2x+y-6=0

RS Aggarwal, Class 10, chapter 3A, question no 15

## x−2y+2=0….(1)

2x+y−6=0……(2)

Isolate x from equation (1) and find the value of x and y.

x−2y+2=0

or x=2y−2

## Similarly, isolate y from equation (2) and find the values of x and y.

2x+y−6=0

or y=6−2x

## Graph:

Both the lines intersect each other at point C(2,2) and y− axis at A(−2,0) and F(3,0)

Now, To find the area of triangle CAF:

Area of △CAF=1/2(base×altitude)

=1/2×5×2

=5 sq.units.