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
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
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.
