Question

Solve the following inequalities graphically in two dimensional plane:

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

Answer 1

The given inequality is $-3x+2y\ge -6$.

Draw the graph of the line $-3x+2y=-6$:

Table of values satisfying the equation $-3x+2y=-6$:
$\begin{array}{ccc}x& 2& 0\\ y& 0& -3\end{array}$

Putting (0,0) in the given inequation, we have $-3\times 0+2\times 0\ge -6$
$\Rightarrow 0\ge -6$ which is true.

$\therefore$ Half plane of $-3x+2y\ge -6$ is towards origin.