Question

Draw the graphs of the following equations on the same graph paper:

$2x-y+2=0,2x+y=6.$

Find the coordinates of the vertices of the shape formed by these lines. Also, find the area of the shape.

Answer 1

Given equations are:

2x + y -6 = 0 ... (1)

2x - y +2 = 0 ... (2)

Solution for 2x + y -6 = 0 are (2, 2), (0, 6) and (3, 0).

Solution for 2x - y + 2 = 0 are (2, 6), (1, 4) and (3, 8).

The graph for the equations can be drawn as follows:

Co-ordinates of vertices are (1, 4), (-1, 0) and (3, 0).

Area = $\frac{1}{2}\times base\times height$

= $\frac{1}{2}\times 4\times 4$

= 8 sq units