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Question
Find the graphical solution of the following system of linear inequations:
2x + y ≥ 8, x + 2y ≥ 10, x ≥ 0, y ≥ 0
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Solution
Writing the above inequalities as equations
2x + y = 8
| x | 0 | 4 |
| y | 8 | 0 |
| (x, y) | (0, 8) | (4, 0) |
x + 2y = 10
| x | 0 | 10 |
| y | 5 | 0 |
| (x, y) | (0, 5) | (10, 0) |
The inequality 2x + y ≥ 8 represents the region above the line, including the points on the line 2x + y = 8
The inequality x + 2y ≥ 10 represents the region above the line, including the points on the line x + 2y = 10
Since x ≥ 0; y ≥ 0, all points in the shaded region represents solution of the given system of inequalities.
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