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Question
Solve the following system of inequalities graphically.
x + y ≤ 9, y > x, x ≥ 0
Solution
To find graphical solution, construct the table as follows:
| Inequation | Equation | Double Intercept form |
Points (x, y) |
Region |
| x + y ≤ 9 | x + y = 9 | `"x"/9 + "y"/9` = 1 | A (9, 0), B (0, 9) |
0 + 0 ≤ 9 ∴ 0 ≤ 9 ∴ origin side |
| y ≥ x | y = x | – | 0 (0, 0), C (1, 1) |
∴ 0 ≥ 0 ∴ origin side |
| x ≥ 0 | x = 0 | – | R.H.S. of Y-axis |
Shaded portion represents the graphical solution.
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