Question

Solve graphically the equations $2x-y=1$; $x+2y=8$

Answer 1

We find three points for each equation, by choosing three values of $x$ and computing the corresponding $y$ values. We'll put our results in tables.
Line 1: $2x-y=1$
$y=2x-1$
Substituting $x=-1,0,1$ in the above equation, we find

$y=2x-1$

$x$	$-1$	$0$	$1$
$2x$	$-2$	$0$	$2$
$y=2x-1$	$-3$	$-1$	$1$

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

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

$x$	$-2$	$0$	$2$
$-\frac{x}{2}$	$1$	$0$	$-1$
$y=-\frac{x}{2}+4$	$5$	$4$	$3$

We plot the points $(-1,-3)$, $(0,-1)$ and $(1,1)$ in a graph sheet and draw the line through them. Next, we plot the points $(-2,5)$, $(0,4)$ and $(2,3)$ in the same graph sheet and draw the line through them. We find that the two graphs are intersecting at the point $(2,3)$. Hence, the system of equations has only one solution (unique solution|) and the solution is $x=2$, $y=3$. Therefore the solution is $(2,3)$.