solve the following systems of inequations graphically :

12 + 12y ≤ 840, 3x + 6y ≤ 300,8x + 4y ≤ 480, x ≥ 0, y ≥ 0

First we will find the solutions of the given equations by hit and trial method and afterwards 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,

12 + 12y ≤ 840

x + y ≤ 70

x | 0 | 35 | 70 |

y | 70 | 35 | 0 |

3x + 6y ≤ 300

x + 2y ≤ 100

x | 0 | 50 | 100 |

y | 50 | 25 | 0 |

8x + 4y ≤ 480

2x + y ≤ 120

x | 0 | 30 | 60 |

y | 120 | 60 | 0 |

x ≥ 0, y ≥ 0

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