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Question
Solve the following system of inequalities graphically.
3x + 4y ≤ 60, x + 3y ≤ 30, x ≥ 0, 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 |
| 3x + 4y ≤ 60 | 3x + 4y = 60 | `"x"/20 + "y"/15` = 1 | A (20, 0), B (0, 15) |
5(0) + 4(0) ≤ 60 ∴ 0 ≤ 60 ∴ origin side |
| x + 3y ≤ 30 | x + 3y = 30 | `"x"/30 + "y"/10` = 1 | C (30, 0), D (0, 10) |
0 + 3 (0) ≤ 30 ∴ 0 ≤ 30 ∴ origin side |
| x ≥ 0 | x = 0 | – | – | R.H.S. of Y-axis |
| y ≥ 0 | y = 0 | – | – | above X-axis |
Shaded portion represents the graphical solution.
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