Question

Solve graphically:

$4x+3y-7=0$

$2x-3y+1=0$

Answer 1

Graph of the equation $4x+3y-7=0$

$\Rightarrow y=\frac{7-4x}{3}$

When $x=-2,y=\frac{7-4\times -2}{3}=\frac{7+8}{3}=5$

When $x=4,y=\frac{7-4\times 4}{3}=\frac{7-16}{3}=-3$

$x$	$-2$	$4$
$y=\frac{7-4x}{3}$	$5$	$-3$

Plot the points $A(-2,5)$ and $B(4,-3)$ on the graph and join these points by a straight line $AB$.The line $AB$ is the graph of the equation $4x+3y-7=$

Graph of the equation $2x-3y+1=0$

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

When $x=-2,y=\frac{2\times -2+1}{3}=\frac{-4+1}{3}=-1$

When $x=4,y=\frac{2\times 4+1}{3}=\frac{8+1}{3}=3$

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

Plot the points $C(-2,-1)$ and $D(4,3)$ on the graph and join these points by a straight line $CD$.The line $CD$ is the graph of the equation $2x-3y+1=0$

The lines $AB$ and $CD$ intersect at the point $P$ whose coordinates are $(1,1)$

The solution is at $(1,1)$