Question

Solve the following inequalities graphically in two-dimensional plane:

$-3x+2y\ge -6$

Answer 1

$-3x+2y\ge -6$

Lets first draw graph of

$x$ $0$ $2$

$y$ $-3$ $0$

$-3x+2y=-6$

Putting $x=0$ in (1)

$-3\left(0\right)+2y=-6$

$0+2y=-6$

$2y=-6$

$y=\frac{-6}{2}$

$y=-3$

Putting $y=0$ in (1)

$-3x+2\left(0\right)=-6$

$-3x+0=-6$

$-3x=-6$

$x=\frac{-6}{-3}$

$x=2$

Drawing graph

$x$ $0$ $2$

$y$ $-3$ $0$

Point to be plotted are $(0,-3),(2,0)$

Checking for $(0,0)$

Putting $x=0,y=0$

$-3x+2y\ge -6$

$-3\left(0\right)+2\left(0\right)\ge -6$

$0\ge -6$

Which is true

Hence origin lies in the plane $-3x+2y\ge -6$.

So, we shade left side of line.