Solve the following systems of inequalities graphically:

$x + y \leq 6, x + y \geq 4$

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Solution

The given inequality is $x + y \leq 6$ .

Draw the graph of the line x + y =6.

Table of values satisfying the equation

x+y=6

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

Putting (0,0) in the given inequation, we have $0 + 0 \leq 6 \Rightarrow 0 \leq 6$ , which is true

$∴$ Half plane of $x + y \leq 6$ is towards origin.

Also the given inequality is $x + y \geq 4$ .

Draw the graph of the line x + y =4.

Table of values satisfying the equation

x+y=4

$\begin{matrix} x & 2 & 1 y & 2 & 3 \end{matrix}$

Putting (0,0) in the given inequation, we have $0 + 0 \geq 4 \Rightarrow 0 \geq 4$ , which is false

$∴$ Half plane of $x + y \geq 4$ is away from origin.

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