Question
Solve the system of inequality graphically: 2x + y $\ge$ 6, 3x + 4y $\le$ 12
✓
Answer
The given inequality is $2x + y \geqslant 6$
Draw the graph of the line 2x + y = 6
Table of values satisfying the equation 2x + y = 6
Draw the graph of the line 2x + y = 6
Table of values satisfying the equation 2x + y = 6
| X | 3 | 2 |
| Y | 0 | 2 |
Putting (0, 0) in the given in equation, we have
$2 \times 0 + 0 \geqslant 6 \Rightarrow 0 \geqslant 6$, which is false.
$\therefore $ Half plane of $2x + y \geqslant 6$ is away from origin.
Also the given inequality is $3x + 4y \leqslant 12$.
Draw the graph of the line 3x + 4y = 12
Table of values satisfying the equation
3 x + 4y = 12
| X | 0 | 4 |
| Y | 3 | 0 |
Putting (0, 0) in the given inequation, we have
$3 \times 0 + 4 \times 0 \geqslant 12 \Rightarrow 0 \leqslant 12$, which is true.
$\therefore $ Half plane of $3x + 4y \leqslant 12$ is towards origin.
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