Show that the following system of linear equations has no solution :

x + 2y ≥ 3, 3x + 4y ≥ 12, x ≥ 0, y ≥ 1.

First, we will find the solutions of the given equations by hit and trial method and afterward we will plot the graph of the equations and shade the side with grey color containing common solutions or intersection of the solution set of each inequality,

You can choose any value but find the two mandatory values which are at x = 0 and y = 0, i.e., x and y–intercepts always,

x + 2y ≥ 3

x | 0 | 1 | 3 |

y | 1.5 | 1 | 0 |

3x + 4y ≥ 12

x | 0 | 2 | 4 |

y | 3 | 1.5 | 0 |

x ≥ 0, y ≥ 1

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