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Question
Solve the following system of inequalities graphically.
2x + y ≥ 6, 3x + 4y ≤ 12
Graph
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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 ≥ 6 | 2x + y = 6 | `"x"/3 + "y"/6` = 1 | A (3, 0) B (0, 6) |
2(0) + 0 `≱ `6 ∴ 0 `≱ `6 ∴ non-origin side |
| 3x + 4y ≤ 12 | 3x + 4y = 12 | `"x"/4 + "y"/3` = 1 | C (4, 0) D (0, 3) |
3(0) + 4(0) ≤ 12 ∴ 0 ≤ 12 ∴ origin side |
The shaded portion represents the graphical solution.
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