Question

Solve the system of equations graphically:
3x + 2y = 4,
2x – 3y = 7

Answer 1

On a graph paper, draw a horizontal line X'OX and a vertical line YOY' representing the x-axis and y-axis, respectively.

Graph of 3x + 2y = 4
3x + 2y = 4
⇒2y = (4 – 3x)
⇒ `y=(4-3x)/2`      …(i)

Putting x = 0, we get y = 2
Putting x = 2, we get y = -1
Putting x = -2, we get y = 5
Thus, we have the following table for the equation 3x + 2y = 4

x	0	2	-2
y	2	-1	5

Now, plot the points A(0, 2), B(2, -1) and C(-2, 5) on the graph paper.
Join AB and AC to get the graph line BC. Extend it on both ways.
Thus, BC is the graph of 3x + 2y = 4.
Graph of 2x - 3y = 7
2x – 3y = 7
⇒ 3y = (2x – 7)
⇒ `y=(2x-7)/3`    …(ii)

Putting x = 2, we get y = -1
Putting x = -1, we get y = -3
Putting x = 5, we get y = 1
Thus, we have the following table for the equation 2x – 3y = 7.

x	0	2	-2
y	2	-1	5

Now, plot the points P(-1, -3) and Q(5, 1). The point C(2, -1) has already been plotted. Join PB and QB and extend it on both ways.
Thus, line PQ is the graph of 2x – 3y = 7.

The two graph lines intersect at B(2, -1).
∴x = 2 and y = -1 are the solutions of the given system of equations.