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Question
Solve the following system of inequalities graphically.
5x + 4y ≤ 20, x ≥ 1, y ≥ 2
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Solution
To find graphical solution, construct the table as follows:
| Inequation | Equation | Double Intercept form |
Points (x, y) |
Region |
| 5x + 4y ≤ 20 | 5x + 4y = 20 | `"x"/4 + "y"/5` = 1 | A (4, 0), B (0, 5) |
5(0) + 4(0) ≤ 20 ∴ 0 ≤ 20 ∴ origin side |
| x ≥ 1 | x = 1 | – | – | ∴ 0 `≱` 1 ∴ R.H.S. of line x = 1 |
| y ≥ 2 | y = 2 | – | – | ∴ 0 `≱` 2 ∴ above the line y = 2 |
The shaded portion represents the graphical solution.
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