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Linear Systems of Inequalities Math Tech II Everette Keller

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

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y ≥ 3x + 4

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

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y = 3x y = x + 4

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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.

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

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

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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

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Write a system of linear inequalities based on the graph.

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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?

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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?

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

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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

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EXAMPLE 4 Graph a linear inequality in one variables Graph the inequality y –3. SOLUTION Graph the equation y = –3. The inequality is , so use a solid.

EXAMPLE 4 Graph a linear inequality in one variables Graph the inequality y –3. SOLUTION Graph the equation y = –3. The inequality is , so use a solid.

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