Solve the following systems of inequalities graphically:

$3 x + 2 y \leq 12, x \geq 1, y \geq 2$

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Solution

The given inequality is $3 x + 2 y \leq 12$ .

Draw the graph of the line 3x +2y =12.

Table of values satisfying the equaiton

3x +2y =12

$\begin{matrix} x & 2 & 4 y & 3 & 0 \end{matrix}$

Putting (0,0) in the given inequation, we have $3 \times 0 + 2 \times 0 \leq 12 \Rightarrow 0 \leq 12$ which is true.

$∴$ Half plane of 3x +2y $\leq$ 12 is towards origin.

Also the given inequality is $x \geq 1$ .

Draw the graph of the line x =1.

Putting (0,0) in the given inequation, we have $0 \geq 1$ which is false.

$∴$ Half plane of x $\geq$ 1 is away from origin. The given inequality is $y \geq 2.$

Draw the graph of the line y =2.

Putting (0,0) in the given inequation, we have $0 \geq 2$ which is false.

$∴$ Half plane of $y \geq 2$ is away from origin.

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