Question
Solve the system of inequality graphically: x + y $\ge$ 4, 2x – y < 0
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Answer
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.
Draw the graph of the line x + y = 4.
Table of values satisfying the equation x + y = 4.
| X | 3 | 2 |
| Y | 1 | 2 |
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.
Also the given inequality is 2x - y < 0
Draw the graph of the line 2x - y = 0
Table of values satisfying the equation 2x - y = 0
| X | 1 | 2 |
| Y | 2 | 4 |
Putting (3, 0) in the given inequation, we have
$2 \times 3 - 0 <0 \Rightarrow 6 <0$, which is false.
$\therefore $ Half plane of 2x - y = 0 does not contain (3, 0)
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