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Solve the following system of inequalities graphically.

3x + 2y ≤ 12, x ≥ 1, y ≥ 2

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#### Solution

To find graphical solution, construct the table as follows:

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

3x + 2y ≤ 12 | 3x + 2y = 12 | `"x"/4 + "y"/6` = 1 | A (4, 0), B (0, 6) |
3(0) + 2(0) ≤ 12 ∴ 0 ≤ 12 ∴ origin side |

x ≥ 1 | x = 1 | – | – | 0 `≱ ` 1 ∴ R.H.S. of line x = 1 |

y ≥ 2 | y = 2 | – | – | 0 `≱` 2 ∴ above line y = 2 |

The shaded portion represents the graphical solution.

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