Question

Solve graphically the pair of equations $x+2y=4$; $2x+4y=8$.

Answer 1

We find three points for each equation, by choosing three values of $x$ and computing the corresponding $y$ values. We show our results in tables.
Line 1: $x+2y=4$
$2y=-x+4\Rightarrow y=-\frac{x}{2}+2$
Substituting $x=-2,0,2$ in the above equation, we get the corresponding $y$ values as

$y=-\frac{x}{2}+2$

$x$	$-2$	$0$	$2$
$-\frac{x}{2}$	$1$	$0$	$-1$
$y=-\frac{x}{2}+2$	$3$	$2$	$1$

Line 2: $2x+4y=8$
$4y=-2x+8\Rightarrow y=-\frac{x}{2}+2$
Substituting $x=-4,0,4$ in the above equation, we get $y$ values as

$y=-\frac{x}{2}+2$

$x$	$-4$	$0$	$4$
$-\frac{x}{2}$	$2$	$0$	$-2$
$y=-\frac{x}{2}+2$	$4$	$2$	$0$

We plot these points in a graph paper and draw the lines. Then we find that both the lines coincide. Any point on one line is also a point on the other. That is all points on the line are common points. Therefore each point on the line is a solution. Hence there are infinitely many solution.