Solve the following systems of inequalities graphically:

$x + y \leq 9 m y > x, x \geq 0$

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Solution

The given inequality is $x + y \leq 9$ .

Draw the graph of the line x+y =9.

Table of values satisfying the equation x+y =9

$\begin{matrix} x & 5 & 4 y & 4 & 5 \end{matrix}$

Putting (0,0) in the given inequation, we have $0 + 0 \leq 9 \Rightarrow 0 \leq 9$ , which is true.

$∴$ Half plane of $x + y \leq 9$ is towards origin.

Also the given inequality is x-y < 0.

Draw the graph of the line x -y =0.

Table of values satisfying the equation x - y =0

$\begin{matrix} x & 1 & 2 y & 1 & 2 \end{matrix}$

Putting (0,3) in the given inequation, we have $0 - 3 < 0 \Rightarrow - 3 < 0$ , which is true.

$∴$ Half plane of x-y < 0 containing the point (0,3)

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