# Solve each of the following systems of equations graphically: 2x + 3y = 2 and x – 2y = 8

### Question

Solve each of the following systems of equations graphically:
2x + 3y = 2
x – 2y = 8

### Solution:

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

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

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.