Graph

Solve the following system of inequalities graphically.

x – 2y ≤ 3, 3x + 4y ≥ 12, x ≥ 0, y ≥ 1

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#### Solution

To find graphical solution, construct the table as follows:

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

x – 2y ≤ 3 | x – 2y = 3 |
`"x"/3 - (2"y")/3` = 1 i.e., `"x"/3 + "y"/(((-3)/2))` = 1 |
A (3, 0), B `(0, (-3)/2)` |
0 – 2(0) ≤ 3 ∴ 0 ≤ 3 ∴ origin side |

3x + 4y ≥ 12 | 3x + 4y = 12 | `"x"/4 + "y"/3` = 1 | C (4, 0), D (0, 3) |
3(0) + 4(0) `≱` 12 ∴ 0 `≱ ` 12 ∴ non-origin side |

x ≥ 0 | x = 0 | – | – | R.H.S. of Y-axis |

y ≥ 1 | y = 1 | – | – | 0 `≱` 1 Above the line y = 1 |

The shaded portion represents the graphical solution.

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