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Question
Find the graphical solution for the system of linear inequation 2x + y ≤ 2, x − y ≤ 1
Solution
To find graphical solution, construct the table as follows:
| Inequation | Equation | Double intercept form |
Points (x, y) |
Region |
| 2x + y ≤ 2 | 2x + y = 2 | `x/1 + y/2` = 1 | A(1, 0) B(0, 2) |
2(0) + 0 ≤ 2 ∴ origin side |
| x − y ≤ 1 | x − y = 1 | `x/1 + y/(-1)` = 1 | A(1, 0) C(0, −1) |
0 - 0 ≤ 1 ∴ origin side |
The shaded portion represents the graphical solution.
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Figure
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