Solve graphically the system of equations
4x – y – 4 = 0
3x + 2y – 14 = 0. Find the coordinates of the vertices of the triangle formed by these two lines and the y-axis.

Solution:

Draw a horizontal line on a graph paper and a vertical line as the -axis and -axis, respectively.
Graph of

Putting , we obtain .
Putting , we obtain .
Putting , we obtain

Therefore, we have the following table for the equation .

   

Now, plot the points and on the graph paper. Join and to get the graph line . Extend it on both ways.

Therefore, is the graph of
Graph of

Putting , we obtain .
Putting , we obtain .
Putting we obtain .

So, we have the following table for the equation .

   

Now, plots the points and . The point has already been plotted. Join and to get the graph line .
Extend it on both ways.

Then, is the graph of the equation .

The two graph lines intersect at .
The solution of the given system of equations is and .

These graph lines intersect the -axis at and .
As a result, the region bounded by these lines and the -axis has been shaded.