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Published byNathan Simon Modified over 4 years ago

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4.3.1 – Systems of Inequalities

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Recall, we solved systems of equations What defined a system? How did you find the solutions to the system?

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Systems of Inequalities A system of linear inequalities has 2 or more linear inequalities Their solutions are any ordered pair that satisfies BOTH inequalities Only method to solve? Graphing

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Solutions To test whether a particular solution, or solution set (x,y) is a solution, we plug the x and y solutions and test both inequalities Example. Check whether (3, -1) is a solution to the system: x + y > 1 y < 2

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Example. Tell whether (4, 2) is a solution to the system: x + y ≤ 2 4x – y > 3

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Example. Tell whether (4, 2) is a solution to the system: x > 1 x + y ≤ 4

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Solving Systems Similar to solving equations, to solve a linear system, we will graph both inequalities on the same plane Remember… = Dashed Line ≤, ≥ = Solid Line >, ≥ = Shade Above (when not in std. form) <, ≤ = Shade Below (when not in std. form)

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Solutions? The solutions are where the shading will overlap Helpful to have 2 colors To check your solution, choose a test point in the overlapping shaded region

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Example. Find the solutions to the system y < 2x – 3 y ≥ -x - 1

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Example. Find the solutions to the system y ≤ x - 4 x ≥ -8

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Example. Find the solutions to the system y ≤ -x + 5 x – y < 4

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Example. Find the solutions to the system x + y > 4 2x – y ≥ 3

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Assignment Pg. 188 3-8 all, 10-18 even

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