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**7.2 Solve Linear Systems by Substitution**

Solve systems of linear equations by substitution. Determine what the “solution” means in a system of equations.

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Solve the equation. 1. 6a – 3 + 2a = 13 ANSWER 2. 4(n + 2) – n = 11 ANSWER

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3. You burned 8 calories per minute on a treadmill and 10 calories per minute on an elliptical trainer for a total of 560 calories in 60 minutes. How many minutes did you spend on each machine? ANSWER

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**A pet store sells angel fish for $6 each and clown loaches for $4 each**

A pet store sells angel fish for $6 each and clown loaches for $4 each. If the pet store sold 8 fish for $36, how many of each type of fish did it sell? 3. ANSWER

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**Use the substitution method**

EXAMPLE 1 Use the substitution method Solve the linear system: y = 3x + 2 Equation 1 x + 2y = 11 Equation 2 SOLUTION

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EXAMPLE 1 Use the substitution method STEP 2 Substitute 3x + 2 for y in Equation 2 and solve for x.

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EXAMPLE 1 Use the substitution method STEP 3 Substitute 1 for x in the original Equation 1 to find the value of y. ANSWER

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EXAMPLE 1 GUIDED PRACTICE Use the substitution method CHECK Substitute 1 for x and 5 for y in each of the original equations.

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**Use the substitution method**

EXAMPLE 2 Use the substitution method Solve the linear system: x – 2y = –6 Equation 1 4x + 6y = 4 Equation 2 SOLUTION

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EXAMPLE 2 Use the substitution method STEP 2 Substitute 2y – 6 for x in Equation 2 and solve for y.

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EXAMPLE 2 Use the substitution method STEP 3 Substitute 2 for y in the revised Equation 1 to find the value of x. ANSWER

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**Use the substitution method**

EXAMPLE 2 GUIDED PRACTICE Use the substitution method CHECK Substitute –2 for x and 2 for y in each of the original equations. Equation 1 Equation 2

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

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

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**Solve a multi-step problem**

EXAMPLE 3 Solve a multi-step problem WEBSITES 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. 21.00 22.00

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

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EXAMPLE 3 Solve a multi-step problem Equation 2: Website hosting company

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EXAMPLE 3 Solve a multi-step problem STEP 2 Substitute 22.00x for y in Equation 1 and solve for x.

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EXAMPLE 1 Solve a system graphically Graph the linear system and estimate the solution. Then check the solution algebraically. 4x + y = 8 2x – 3y = 18.

EXAMPLE 1 Solve a system graphically Graph the linear system and estimate the solution. Then check the solution algebraically. 4x + y = 8 2x – 3y = 18.

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