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Ch 5.1 Graphing Systems Objective: To solve a system of linear equations by graphing.

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Definition 1)Graph both equations using any method (Table, Intercept, Slope-Intercept) 2)The (x, y) coordinate where the lines intersect is the solution. Rules System (of equations): Two or more equations involving the same variables. Check Your Answers! Plug in the x and y solutions into BOTH equations to verify that they both make TRUE statements.

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y = 2x - 1 y = -x + 5 Example 1 2121 rise run rise run 1

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y = -x - 1 y = x + 2 1212 Example 2 1 rise run rise run 1212

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y = x + 1 2323 y = x - 4 6 Example 3 2323 rise run rise run 6

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Check! y = x + 2 y = x - 2 -2 3 1414 Example 4 -2 3 rise run rise run 1414

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Pam has $120 and is spending $5 every week. Lorenzo has $20 and is saving $7.50 every week. When will they have the same amount of money? Let x = # of weeks Let y = total money Pam Lorenzo weeks total money 0 2 4 6 8 10 120 100 80 60 40 20 0 In 8 weeks -5 1 -10 2 = 7.5 1 15 2 = 30 4 =

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Classwork y = - x + 4 y = x - 4 1) y = - x - 3 y = -2x + 2 2)

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y = 5x - 2 y = -x + 4 3) x + y = 3 7x + y = -3 4)

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x + y = -3 6x + y = 2 5) 3x + y = 4 x - 2y = 6 6)

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