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Question
Solve the following system of inequalities graphically.
2x – y ≥ 1, x – 2y ≤ – 1
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Solution
To find graphical solution, construct the table as follows:
| Inequation | Equation | Double Intercept form |
Points (x, y) |
Region |
| 2x – y ≥ 1 | 2x – y = 1 |
`(2"x")/1 - "y"/1` = 1 i.e., `"x"/(1/2) + "y"/(-1)` = 1 |
A `(1/2, 0)` B (0, – 1) |
2(0) – 0 `≱ ` 1 ∴ 0 `≱ ` 1 ∴ non-origin side |
| x – 2y ≤ – 1 | x – 2y = – 1 |
`"x"/(-1) - (2"y")/(-1)` = 1 i.e., `"x"/(-1) + "y"/((1/2))` = 1 |
C (– 1, 0), D `(0, 1/2)` |
0 – 2(0) `≰ ` – 1 ∴ 0 `≰` – 1 ∴ non-origin side |
The shaded portion represents the graphical solution.
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