Question
Solve the inequality graphically in a two-dimensional plane: 2x + y $\ge$ 6
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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 | 1 | 2 |
| Y | 4 | 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 always from origin
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