Chapter I : Linear Equations in two variables in two variables

Example 13. Draw the graphs of the equations

and

Deter mine the vertices of the triangle formed by the lines representing these equations and the x-axils. Shade the triangular region so formed.

Solution: - Let us take the equation

When,

When,

When,

x	o	1	2
y	-4	0	4

We plot the points (0, -4), (1, 0) and (2, 4) on the graph paper and join them. We get a straight line. Now we take the line AB.

4x + y = 121

When x = 2, y = 12 - 4 x 2 = 4

When x = 3, y = 12 - 4 x 3 = 0

When x = 4, y = 12 - 4 x 4 = -4.

x	2	3	4
y	4	0	-4

We plot the points (2, 4) (3, 0) and (4, -4) on the same graph paper. on joining them we get a line CD which intersect previous line AB. at P (2, 4)

AB intersects the x-axis at (1, 0) and CD intersects the x-axis at (3, 0)

Hence the vertices of the triangle PBD are (2, 4), (1, 0) and (3, 0) . The required region is shaded.