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Question
Solve the following system of inequalities graphically.
x + 2y ≤ 10, x + y ≥ 1, x – y ≤ 0, x ≥ 0, y ≥ 0
Solution
To find graphical solution, construct the table as follows:
| Inequation | Equation | Double Intercept form |
Points (x, y) |
Region |
| x + 2y ≤ 10 | x + 2y = 10 | `"x"/10 + "y"/5` = 1 | A (10, 0), B (0, 5) |
0 + 2(0) ≤ 10 ∴ 0 ≤ 10 ∴ origin side |
| x + y ≥ 1 | x + y = 1 | `"x"/1 + "y"/1` = 1 | C (1, 0), D (0, 1) |
0 + 0 `≱` 1 ∴ 0 `≱` 1 ∴ non-origin side |
| x – y ≤ 0 | x – y = 0 | – | 0 (0, 0), E(1, 1) |
0 – 0 ≤ 0 ∴ 0 ≤ 0 ∴ origin side |
| 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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