Question

Solve the following system of inequalities graphically:
$x+y\ge 4,2x-y<0$

Answer 1

Given $x+y\ge 4,2x-y<0$
First, we solve $x+y\ge 4$
Let’s draw graph of $x+y=4$ $\dots .\left(1\right)$

Putting $y=0$ in equation $\left(1\right)$	Putting $x=0$ in equation $\left(1\right)$
$\Rightarrow x+0=4$	$\Rightarrow y+0=4$
$\Rightarrow x=4$	$\Rightarrow y=4$

Hence,

$x$	$4$	$0$
$y$	$0$	$4$

Now, we solve $2x-y<0$
Lets's draw graph of $2x-y=0$ $....\left(2\right)$

Putting $y=0$ in equation $\left(2\right)$	Putting $x=1$ in equation $\left(2\right)$
$\Rightarrow 2x-0=0$	$\Rightarrow 2\left(1\right)-y=0$
$\Rightarrow 2x=0$	$\Rightarrow 2-y=0$
$\Rightarrow x=0$	$\Rightarrow y=2$

Hence,

$x$	$0$	$1$
$y$	$0$	$2$

Solve for required region:
$x+y\ge 4,2x-y<0$

Taking common region that satisfies all the given inequalities .