Question

Check graphically whether the pair of linear equation 4x − y − 8 = 0 and 2x − 3y + 6 = 0 is consistent. Also, find the vertices of the triangle formed by these lines with the x-axis.

Answer 1

Here we have to draw the graph between two equations given by

Also we have to find the vertices of the triangle form by the x-axis and these lines.

The first equation can written as follow

Now we are going to find the value of y at different value of x

x	2	3
y	0	4

Now mark the points (0,-8) and (2, 0) on xy −plane and we will draw a line which passes through these two points.

The second equation can be written as

x	0	3
y	2	4

Now mark the points (0, 2) and (3, 4) on xy −plane and we will draw a line which passes through these two points.

From the above analysis, we have the following graph

From the above graph the vertices A, B and C are given as follow.

Hence the vertices are