# Linear Systems of Inequalities Math Tech II Everette Keller.

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Linear Systems of Inequalities Math Tech II Everette Keller

A statement that two quantities are either unequal or equal while being greater than or less than a specific quantity

y ≥ 3x + 4

Two or more linear inequalities in the same variables form a system of linear inequalities, or a system of inequalities.

y = 3x y = x + 4

A solution of a system of linear inequalities in two variables is an ordered pair that is a solution of each inequality in the system.

Find the solution to the linear system by graphing x + y < 4 x + 4y ≥ 0

Find the solution to the linear system by graphing x + 2y ≤ 6 -x + y < 0

Step 1 – Graph the boundary lines of each inequality. Use a dashed line if the inequality is and a solid line if the inequality is ≥ or ≤ Step 2 – Shade the appropriate half-plane for each inequality Step 3 – Identify the solution of the system of inequalities as the intersection of the half-planes from Step 2

Write a system of linear inequalities based on the graph.

Set up a system to find the solution A farmer has 10 acres to plant in wheat and rye. He has to plant at least 7 acres. However, he has only \$1200 to spend and each acre of wheat costs \$200 to plant and each acre of rye costs \$100 to plant. Moreover, the farmer has to get the planting done in 12 hours and it takes an hour to plant an acre of wheat and 2 hours to plant an acre of rye. If the profit is \$500 per acre of wheat and \$300 per acre of rye how many acres of each should be planted to maximize profits?

1.Explain to me what a system of linear inequalities is. 2.Can there be more than one solution that occurs? 3.How many solutions can occur? 4.How do you know what the best possible solution is?

What are the optimal solutions of a system and why do they occur?

Find a real life problem that relates to systems of linear inequalities and state it for the next class period Problems 1 – 10 on the Handout