Question

Solve the system of equations graphically:
x + 2y + 2 = 0
3x + 2y -2=0

Answer 1

On a graph paper, draw a horizontal line X'OX and a vertical line YOY' as the x-axis and y-axis, respectively.
                          Graph of 2x + 3y = 4
x + 2y + 2 = 0
⇒2y = (–2 – x)
∴ `y = (-2-x)/2`               …(i)
Putting x = -2, we get y = 0.
Putting x = 0, we get y = -1.
Putting x = 2, we get y = -2.
Thus, we have the following table for the equation x + 2y + 2 = 0.

x	-2	0	2
y	0	-1	-2

Now, plot the points A (-2, 0), B (0, -1) and C (2, -2) on the graph paper.
Join AB and BC to get the graph line AC. Extend it on both ways.
Thus, AC is the graph of x + 2y + 2 = 0.
                          Graph of 3x + 2y - 2 = 0
3x + 2y – 2 = 0
⇒ 2y = (2 – 3x)
∴` y = (2 -3x)/2`    ……..(ii)
Putting x = 0, we get y = 1.
Putting x = 2, we get y = -2.
Putting x = 4, we get y = -5.
Thus, we have the following table for the equation 3x + 2y – 2 = 0.

x	0	2	4
y	1	-2	-5

Now, plot the points P (0, 1) and Q(4, -5). The point C(2, -2) has already been plotted. Join PC and QC and extend it on both ways.
Thus, PQ is the graph of 3x + 2y – 2 = 0.

The two graph lines intersect at A(2, -2).
∴x = 2 and y = -2.