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Question
Solve the following system of inequalities graphically.
3x + 2y ≤ 150, x + 4y ≥ 80, x ≤ 15, y ≥ 0, x ≥ 0
Solution
To find graphical solution, construct the table as follows:
| Inequation | Equation | Doule Intercept form | Points (x, y) |
Region |
| 3x + 2y ≤ 150 | 3x + 2y = 150 | `"x"/50 + "y"/75` = 1 | A (50, 0), B (0, 75) |
3(0) + 2(0) ≤ 150 ∴ 0 ≤ 150 ∴ origin side |
| x + 4y ≥ 80 | x + 4y = 80 | `"x"/80 + "y"/20` = 1 | C (80, 0), D (0, 20) |
0 + 4(0) `≱` 80 ∴ 0 `≱` 80 ∴ non-origin side |
| x ≤ 15 | x = 15 | – | – | 0 ≤ 15 ∴ L.H.S. of the line x = 15 |
| x ≥ 0 | x = 0 | – | – | R.H.S. of Y-axis |
| y ≥ 0 | y = 0 | – | – | Above X-axis |
The shaded portion represents the graphical solution.
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