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Question
Solve the following system of inequalities graphically.
x + y ≥ 4, 2x – y ≤ 0
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Solution
To find graphical solution, construct the table as follows:
| Inequation | Equation | Double Intercept form | Points (x, y) | Region |
| x + y ≥ 4 | x + y = 4 | `"x"/4 + "y"/4` = 1 | A (4, 0), B (0, 4) |
0 + 0 `≱ `4 ∴ 0 `≱ `4 ∴ non-origin side |
| x – y ≤ 0 | 2x – y = 0 | – | O (0, 0), D (2, 4) |
2(0) – 0 ≤ 0 ∴ 0 ≤ 0 ∴ origin side |
The shaded portion represents the graphical solution.
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