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Section 7-6: Systems of Inequalities

Section 7-6: Systems of Inequalities. Objectives: (1) To solve systems of linear inequalities (2) To model real-world situations using systems of linear inequalities. Definitions. Two or more linear inequalities together form a system of linear inequalities.

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Section 7-6: Systems of Inequalities

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  1. Section 7-6: Systems of Inequalities Objectives: (1) To solve systems of linear inequalities (2) To model real-world situations using systems of linear inequalities

  2. Definitions • Two or more linear inequalities together form a system of linear inequalities. • A solution to a system of linear inequalities makes each inequality in the system true.

  3. Solving a System of Linear Inequalities • Step 1: Graph the first linear inequality. • Step 2: Shade in the appropriate region. • Step 3: Graph the second linear inequality. • Step 4: Shade in the appropriate region. • Step 5: Solution is the region shaded by both inequalities.

  4. Solve: y > 2x – 5 3x + 4y < 12 3x < 12 3 3 x < 4 4y < 12 4 4 y < 3 Graphing the 1st equation is simple. But to graph the 2nd equation, we must find the intercepts. That’s the x-intercept That’s the y-intercept Example #1

  5. Graph y > 2x – 5 Graph 3x + 4y < 12

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