Question

Solve graphically:$2x+y-7=0,x+3y-11=0$

Answer 1

Here we have

$2x+y-7=0$ .....$\left(1\right)$

$x+3y-11=0$ .....$\left(2\right)$

For linear equation $\left(1\right)$, we will prepare a table of coordinates of the points:

$y=-2x+7$

If $x=1\Rightarrow y=-2\times 1+7=-2+7=5$

If $x=3\Rightarrow y=-2\times 3+7=-6+7=1$

If $x=5\Rightarrow y=-2\times 5+7=-10+7=-3$

$x$	$1$	$3$	$5$
$y$	$5$	$1$	$-3$
points	$A$	$B$	$C$

For linear equation $\left(2\right)$, we will prepare a table of coordinates of the points:

$y=\frac{11-x}{3}$

If $x=1\Rightarrow y=\frac{11+1}{3}=\frac{12}{3}=4$

If $x=5\Rightarrow y=\frac{11-5}{3}=\frac{6}{3}=2$

If $x=8\Rightarrow y=\frac{11-8}{3}=\frac{3}{3}=1$

$x$	$-1$	$5$	$8$
$y$	$4$	$2$	$1$
points	$D$	$E$	$F$

The graph of $2x+y-7=0$ is a straight line $AC$

The graph of $x+3y-11=0$ is a straight line $DF$

These lines intersect at the point $G(2,3)$