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Published byKenyon Hatfield Modified over 2 years ago

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Do Now: Pass out calculators. Pick up an Algebra I sheet from the back – work on Mac & Tolley’s Road Trip problem.

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Objective: To solve a system of equations using substitution.

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EXAMPLE 1 Use the substitution method Solve the linear system: y = 3x + 2 Equation 2 Equation 1 x + 2y = 11 Solve for y. Equation 1 is already solved for y. SOLUTION STEP 1

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EXAMPLE 1 Use the substitution method 7x + 4 = 11 Simplify. 7x = 7 Subtract 4 from each side. x = 1 Divide each side by 7. Substitute 3x + 2 for y. x + 2(3x + 2) = 11 Write Equation 2. x + 2y = 11 Substitute 3x + 2 for y in Equation 2 and solve for x. STEP 2

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EXAMPLE 1 Use the substitution method ANSWER The solution is (1, 5). Substitute 1 for x in the original Equation 1 to find the value of y. y = 3x + 2 = 3(1) + 2 = 3 + 2 = 5 STEP 3

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GUIDED PRACTICE CHECK y = 3x + 2 5 = 3(1) + 2 ? 5 = 5 Substitute 1 for x and 5 for y in each of the original equations. x + 2y = 11 1 + 2 (5) = 11 ? 11 = 11 EXAMPLE 1 Use the substitution method

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EXAMPLE 2 Use the substitution method Solve the linear system : x – 2y = –6 Equation 1 4x + 6y = 4 Equation 2 SOLUTION Solve Equation 1 for x. x – 2y = –6 Write original Equation 1. x = 2y – 6 Revised Equation 1 STEP 1

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EXAMPLE 2 Use the substitution method Substitute 2y – 6 for x in Equation 2 and solve for y. 4x + 6y = 4 Write Equation 2. 4(2y – 6) + 6y = 4 Substitute 2y – 6 for x. Distributive property 8y – 24 + 6y = 4 14y – 24 = 4 Simplify. 14y = 28 Add 24 to each side. y = 2 Divide each side by 14. STEP 2

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EXAMPLE 2 Use the substitution method Substitute 2 for y in the revised Equation 1 to find the value of x. x = 2y – 6 Revised Equation 1 x = 2(2) – 6 Substitute 2 for y. x = –2 Simplify. ANSWER The solution is (–2, 2). STEP 3

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4( –2) + 6 (2) = 4 ? GUIDED PRACTICE CHECK –2 – 2(2) = –6 ? –6 = –6 Substitute –2 for x and 2 for y in each of the original equations. 4x + 6y = 4 4 = 4 Equation 1 Equation 2 x – 2y = –6 EXAMPLE 2 Use the substitution method

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EXAMPLE 1 Use the substitution method Solve the linear system using the substitution method. 3x + y = 10 y = 2x + 5 1. GUIDED PRACTICE for Examples 1 and 2 ANSWER (1, 7)

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EXAMPLE 2 Use the substitution method x + 2y = –6 GUIDED PRACTICE for Examples 1 and 2 x – y = 3 2. ANSWER (0, –3) Solve the linear system using the substitution method.

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EXAMPLE 2 Use the substitution method –2x + 4y = 0 GUIDED PRACTICE for Examples 1 and 2 3x + y = –7 3. Solve the linear system using the substitution method. ANSWER (–2, –1)

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EXAMPLE 3 Solve a multi-step problem Many businesses pay website hosting companies to store and maintain the computer files that make up their websites. Internet service providers also offer website hosting. The costs for website hosting offered by a website hosting company and an Internet service provider are shown in the table. Find the number of months after which the total cost for website hosting will be the same for both companies. WEBSITES

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Solve a multi-step problem EXAMPLE 3 SOLUTION Write a system of equations. Let y be the total cost after x months. Equation 1 : Internet service provider y = 10 + 21.95 x STEP 1

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Solve a multi-step problem EXAMPLE 3 Equation 2 : Website hosting company y = 22.45 x The system of equations is: y = 22.45x Equation 1 y = 10 + 21.95x Equation 2

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Solve a multi-step problem EXAMPLE 3 Substitute 22.45x for y in Equation 1 and solve for x. y = 10 + 21.95x 22.45x = 10 + 21.95x 0.5x = 10 x = 20 The total cost will be the same for both companies after 20 months. ANSWER STEP 2 Write Equation 1. Substitute 22.45x for y. Subtract 21.95x from each side. Divide each side by 0.5.

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