Question

Solve the following system of linear equations graphically. Also, find the coordinates of the points where the lines meet the $y-$ axis.

$2x-y-5=0$

$x-y-3=0$

Answer 1

Given lines: $2x-y-5=0$ and $x-y-3=0$

The line $2x-y-5=0$ can be written as $y=2x-5$ $...\left(1\right)$

$x$	0	1	3
$y$	-5	-3	1

The line $x-y-3=0$ can be written as $x=3+y$ $...\left(2\right)$

$x$	0	3	4
$y$	-3	0	1

Let us substitute $x=3+y$ in equation $\left(1\right)$

$\Rightarrow 2(3+y)-y-5=0$

$\Rightarrow 6+2y-y-5=0$

$\Rightarrow y=-1$

$\therefore x=2$

$\therefore$ The lines meet at the point $(2,-1)$

The coordinates where the lines meet $y-$ axis are $(0,-3)$ and $(0,-5).$