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Question
Solve the following system of inequalities graphically.
2x + y ≥ 4, x + y ≤ 3, 2x – 3y ≤ 6
Solution
To find graphical solution, construct the table as follows:
| Inequation | Equation | Double Intercept form |
Points (x, y) |
Region |
| 2x + y ≥ 4 | 2x + y = 4 | `"x"/2 + "y"/4` = 1 | A (2, 0), B (0, 4) |
2(0) + 0 `≱ ` 4 ∴ 0 `≱ ` 4 ∴ non-origin side |
| x + y ≤ 3 | x + y = 3 | `"x"/3 + "y"/3` = 1 | C (3, 0), D (0, 3) |
0 + 0 ≤ 3 ∴ 0 ≤ 3 ∴ origin side |
| 2x – 3y ≤ 6 | 2x – 3y = 6 |
`"x"/3 - "y"/2` = 1 i.e., `"x"/3 + "y"/(-2)` = 1 |
C (3, 0), E (0, – 2) |
2(0) – 3(0) ≤ 6 ∴ 0 ≤ 6 ∴ origin side |
The shaded portion represents the graphical solution.
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