Question

Solve $3x+2y>6$ graphically.

Answer 1

Solving inequation for graph
Given $3x+2y>6$
Let first draw graph of $3x+2y=6$ $....\left(1\right)$

Putting $x=0$ in equation $\left(1\right)$	Putting $y=0$ in equation $\left(1\right)$
$\Rightarrow 3\left(0\right)+2y=6$	$\Rightarrow 3x+2\left(0\right)=6$
$\Rightarrow 2y=6$	$\Rightarrow 3x=6$
$\Rightarrow y=3$	$\Rightarrow x=2$

Hence,

Drawing graph.

Points to be plotted are $(0,3),(2,0)$


Solve for Required region
Checking for origin $(0,0)$
Putting $x=0,y=0$ in the given inequality,
$3x+2y>6$
$3\left(0\right)+2\left(0\right)>6$
$0>6$ (False)
$\therefore \text{Origin does not lie in plane}3x+2y>6$
So, we shade right side of line $3x+2y=6$
which does not contain origin.

Final answer :