Solving Systems of Linear Inequalities

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Linear Inequalities in 2 Variables

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Presentation transcript:

Solving Systems of Linear Inequalities Mrs. Book Liberty Hill Middle School Algebra

Systems of Linear Inequalities A system of linear inequalities is a set of two or more linear inequalities in the same variables. 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.

Example 1 Tell whether the ordered pair is a solution of the system of linear inequalities y < 2x y ≥ x + 1 (3, 5) Substitute 3 for x and 5 for y in each inequality Yes, it is a solution to each inequality so it is a solution to the system of linear inequalities

Example 1 Tell whether the ordered pair is a solution of the system of linear inequalities y < 2x y ≥ x + 1 (-2, 0) It is not a solution for each inequality. No, it is not a solution of the system.

Graphing Systems of Linear Inequalities Step 1: Graph each inequality in the same coordinate plane Step 2: Find the intersection of the half-planes that are solutions of the inequalities this intersection is the graph of the system.

Lines & Shading < or > dashed line ≤ or ≥ solid line

Write a system of inequalities for the graph x > 5 y ≥ -x + 3

Write a system of inequalities for the graph y ≥ ⅕x – 3 y ≤ -⅔ - 4

Solve each system of inequalities by graphing y > ¼x y ≤ -x + 4

Solve each system of inequalities by graphing y < 2x + 4 -3x – 2y ≥ 6