Question

Draw the graphs of the equations: 4x – y – 8 = 0 and 2x - 3y + 6 = 0. Also determine the vertices of the triangle formed by the lines and the x-axis.

Answer 1

I hope it will help you..

Answer 2

Given

The line 4x – y – 8 = 0 and 2x - 3y + 6 = 0.

To find

We have to find the vertices of the triangle made by given lines and the  x-axis.

Solutions

First consider the line 4x – y – 8 = 0.

If it intercepts x-axis then y =0

So, 4x – 0 – 8 =0

                   4x = 8

                     x = 8/4

                      x = 2.

Now consider the line 2x - 3y + 6 = 0

If it intercepts x-axis then y =0

So ,  2x - 3y + 6 = 0

       2x -3(0) +6 = 0

                     2x  = -6

                        x = -6/2

                        x = -3

Now determine these lines intercept point.

For line 4x – y – 8 = 0

                            y = 4x – 8   ......(1)

Substitute this value in line 2x - 3y + 6 = 0

then, 2x - 3y + 6 = 0

2x - 3(4x – 8) + 6 = 0

    2x - 12x +24 +6 = 0

                -10x +30 = 0

                            x = 3

For y intersect cordinate substitute x=3

then from equ(1)

y = 4(3) -8

y = 12 - 8

y = 4

Hence the vertices of the triangle is (2,0), (-3,0) and (3,4) and the graph is below