Question

Solve each of the following given systems of equations graphically and find the vertices and area of the triangle formed by these lines and the y-axis:
$2x-3y=12,x+3y=6.$

Answer 1

The given systems of equations are:

$2x-3y=12x+3y=6$

Now, x+3y=6

$y=\frac{6-x}{3}$

When x=0 then, y=2

When x=3 then y=1

Thus, we have the following table

X	0	3
Y	2	1

Now, 2x-3y=12

$y=\frac{2x-12}{3}$

When x=0 then, y=-4

When x=6 then y=0

Thus, we have the following table

X	0	6
Y	-4	0

Graph of the given system of equations are :

Clearly, the two lines meet the y-axis at (0,2) and (0,-4) respectively.

Hence the required coordinates are (6,0), (0,2) and (0,-4)