Question

Solve the system of equations graphically:
2x + 3y = 2,
x – 2y = 8

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 2x + 3y = 2

  2x + 3y = 2
⇒3y = (2 – 2x)
⇒3y = 2(1 – x)
⇒ `y=(2(1-x))/3`      …(i)
Putting x = 1, we get y = 0
Putting x = -2, we get y = 2
Putting x = 4, we get y = -2
Thus, we have the following table for the equation 2x + 3y = 2

X	1	-2	4
y	0	2	-2

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

Graph of x - 2y = 8
x – 2y = 8
⇒ 2y = (x – 8)
⇒ `y=(x-8)/2`    …(ii)
Putting x = 2, we get y = -3
Putting x = 4, we get y = -2
Putting x = 0, we get y = -4
Thus, we have the following table for the equation x – 2y = 8.

X	2	4	0
y	-3	-2	-4

Now, plot the points P(0, -4) and Q(2, -3). The point C(4, -2) has already been plotted. Join PQ and QC and extend it on both ways.
Thus, line PC is the graph of x – 2y = 8.

The two graph lines intersect at C(4, -2).
∴ x = 4 and y = -2 are the solutions of the given system of equations.