$2 x+3 y=2$
$x-2 y=8$
On a graph paper, draw a horizontal line X'OX and a vertical line YOY' representing the x-axis and y-axis, respectively.
2x + 3y = 2
⇒ 3y = (2 − 2x)
⇒ 3y = 2(1 − x)
$\Rightarrow y=\frac{2(1-x)}{3}$ .......(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.
x − 2y = 8
⇒ 2y = ( x − 8)
$\Rightarrow y=\frac{x-8}{2}$ ......(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.
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