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Graph

Solve the following system of inequalities graphically.

2x + y ≥ 8, x + 2y ≥ 10

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#### Solution

To find graphical solution, construct the table as follows:

Inequation |
Equation |
Double Intercept form |
Points (x, y) |
Region |

2x + y ≥ 8 | 2x + y = 8 | `"x"/4 + "y"/8` = 1 | A (4, 0), B (0, 8) |
2(0) + 0 `≱ ` 8 ∴ 0 `≱ ` 8 ∴ non-origin side |

x + 2y ≥ 10 | x + 2y = 10 | `"x"/10 + "y"/5` = 1 | C (10, 0), D (0, 5) |
0 + 2(0) `≱` 10 ∴ 0 `≱ ` 10 ∴ non-origin side |

The shaded portion represents the graphical solution.

Concept: Graphical Solution of Linear Inequality of Two Variable

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