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प्रश्न
Find the graphical solution of the following system of linear inequations:
3x + 2y ≤ 24, 3x + y ≥ 15, x ≥ 4
उत्तर
Writing the above inequalities as equations
3x + 2y ≤ 24
| x | 0 | 8 |
| y | 12 | 0 |
| (x, y) | (0, 12) | (8, 0) |
3x + y ≥ 15
| x | 0 | 5 |
| y | 15 | 0 |
| (x, y) | (0, 15) | (5, 0) |
x ≥ 4
| x | 4 | 4 |
| y | 0 | 1 |
| (x, y) | (4, 0) | (4, 1) |
The inequality 3x + 2y ≤ 24 represents the region below the line including the points on the line 3x + 2y = 24.
The inequality 3x + y ≥ 15 represents the region above the line, including the points on the line 3x + y = 15.
The inequality x ≥ 4 repyesents the region to the right of the line, including the points on the line x = 4.
∴ The shaded region between the lines represents the solution of the given inequality.
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