Presentation on theme: "7.2 Solve Linear Systems by Substitution"— Presentation transcript:
17.2 Solve Linear Systems by Substitution Solve systems of linear equations by substitution.Determine what the “solution” means in a system of equations.
2Solve the equation.1. 6a – 3 + 2a = 13ANSWER2. 4(n + 2) – n = 11ANSWER
33. 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
4A 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
6Use the substitution method EXAMPLE 1Use the substitution methodSolve the linear system:y = 3x + 2Equation 1x + 2y = 11Equation 2SOLUTION
7EXAMPLE 1Use the substitution methodSTEP 2Substitute 3x + 2 for y in Equation 2 and solve for x.
8EXAMPLE 1Use the substitution methodSTEP 3Substitute 1 for x in the original Equation 1 to find the value of y.ANSWER
9EXAMPLE 1GUIDED PRACTICEUse the substitution methodCHECKSubstitute 1 for x and 5 for y in each of the originalequations.
10Use the substitution method EXAMPLE 2Use the substitution methodSolve the linear system:x – 2y = –6Equation 14x + 6y = 4Equation 2SOLUTION
11EXAMPLE 2Use the substitution methodSTEP 2Substitute 2y – 6 for x in Equation 2 and solve for y.
12EXAMPLE 2Use the substitution methodSTEP 3Substitute 2 for y in the revised Equation 1 to find the value of x.ANSWER
13Use the substitution method EXAMPLE 2GUIDED PRACTICEUse the substitution methodCHECKSubstitute –2 for x and 2 for y in each of the originalequations.Equation 1Equation 2
14EXAMPLE 1GUIDED PRACTICEUse the substitution methodfor Examples 1 and 2Solve the linear system using the substitution method.y = 2x + 51.3x + y = 10ANSWER
15EXAMPLE 2GUIDED PRACTICEUse the substitution methodfor Examples 1 and 2Solve the linear system using the substitution method.3x + y = –73.–2x + 4y = 0ANSWER
16Solve a multi-step problem EXAMPLE 3Solve a multi-step problemWEBSITESMany 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.21.0022.00
17EXAMPLE 3Solve a multi-step problemSOLUTIONSTEP 1Write a system of equations. Let y be the totalcost after x months.Equation 1: Internet service provider
18EXAMPLE 3Solve a multi-step problemEquation 2: Website hosting company
19EXAMPLE 3Solve a multi-step problemSTEP 2Substitute 22.00x for y in Equation 1 and solvefor x.