Question
Solve the system of inequality graphically: x + y $\le$ 6, x + y $\ge$ 4
✓
Answer
The given in equality is $x + y \leqslant 6$
Draw the graph of the line x + y = 6.
Table of values satisfying the equation x + y = 6
Draw the graph of the line x + y = 6.
Table of values satisfying the equation x + y = 6
| X | 3 | 4 |
| Y | 3 | 2 |
Putting (0, 0) in the given inequation, we have
$0 + 0 \leqslant 6 \Rightarrow 0 \leqslant 6$, which is true.
$\therefore $ Half plane of $x + y \leqslant 6$ is towards origin.
Also the given inequality is $x + y \geqslant 4$
Draw the graph of the line x + y = 4
Table of values satisfying the equation x + y = 4
| X | 2 | 1 |
| Y | 2 | 3 |
Putting (0, 0) in the given inequation, we have
$0 + 0 \geqslant 4 \Rightarrow 0 \geqslant 4$, which is false
$\therefore $ Half plane of $x + y \geqslant 4$ is away from origin.
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