Question
Solve the system of inequality graphically: 2x – y >1, x – 2y < –1
✓
Answer
The given inequality is 2x - y > 1
Draw the graph of the line 2x - y = 1
Table of values satisfying the equation
2x - y = 1
Draw the graph of the line 2x - y = 1
Table of values satisfying the equation
2x - y = 1
| X | 1 | 2 |
| Y | 1 | 3 |
Putting (0, 0) in the given inequation, we have
$2 \times 0 - 0 > 1 \Rightarrow 0 > 1$, which is false.
$\therefore $ Half plane of 2x - y > 1 is away from origin.
Also the given inequality is x - 2y < -1
Draw the graph of the line x - 2y = -1
Table of values satisfying the equation x - 2y = -1
| X | 1 | 2 |
| Y | 1 | 2 |
Putting (0, 0) in the given inequation, we have
$0 - 2 \times 0 < - 1 \Rightarrow 0 < - 1$ which is false
$\therefore $ Half plane of x - 2y < - 1 is away from origin.
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