Question

Solve the following system of linear inequalities graphically: $x+y\ge 5,x-y\le 3$.

Answer 1

Solve inequation for graph :
Given $x+y\ge 5,x-y\le 3$
First, we solve $x+y\ge 5$
Let’s draw graph of $x+y=5$ $\dots .\left(1\right)$

Putting $y=0$ in equation $\left(1\right)$	Putting $x=0$ in equation $\left(1\right)$
$\Rightarrow x+0=5$	$\Rightarrow 0+y=5$
$\Rightarrow x=5$	$\Rightarrow y=5$

Hence,

$x$	$0$	$5$
$y$	$5$	$0$

Now, we solve $x-y\le 3$
Let’s draw graph of $x-y=3$ $\dots .\left(2\right)$

Putting $x=0$ in equation $\left(2\right)$	Putting $y=0$ in equation $\left(2\right)$
$\Rightarrow 0-y=3$	$\Rightarrow x-0=3$
$\Rightarrow y=-3$	$\Rightarrow x=3$

Hence,

$x$	$0$	$3$
$y$	$-3$	$0$

Drawing graph :
Solving for required region : $x+y\ge 5$
$x-y\le 3$
Taking common region that satisfies both the inequalities.