Presentation on theme: "Do Now: Pass out calculators."— Presentation transcript:
1Do Now: Pass out calculators. Pick up an Algebra I sheet from the back – work on Mac & Tolley’s Road Trip problem.
2Objective:To solve a system of equations using substitution.
3Use the substitution method EXAMPLE 1Use the substitution methodSolve the linear system:y = 3x + 2Equation 1x + 2y = 11Equation 2SOLUTIONSTEP 1Solve for y. Equation 1 is already solved for y.
4Use the substitution method EXAMPLE 1Use the substitution methodSTEP 2Substitute 3x + 2 for y in Equation 2 and solve for x.x + 2y = 11Write Equation 2.x + 2(3x + 2) = 11Substitute 3x + 2 for y.7x + 4 = 11Simplify.7x = 7Subtract 4 from each side.x = 1Divide each side by 7.
5EXAMPLE 1Use the substitution methodSTEP 3Substitute 1 for x in the original Equation 1 to find the value of y.y = 3x + 2 = 3(1) + 2 = = 5ANSWERThe solution is (1, 5).
6Use the substitution method EXAMPLE 1GUIDED PRACTICEUse the substitution methodCHECKSubstitute 1 for x and 5 for y in each of the originalequations.y = 3x + 2x + 2y = 115 = 3(1) + 2?1 + 2 (5) = 11?5 = 511 = 11
7Use the substitution method EXAMPLE 2Use the substitution methodSolve the linear system:x – 2y = –6Equation 14x + 6y = 4Equation 2SOLUTIONSTEP 1Solve Equation 1 for x.x – 2y = –6Write original Equation 1.x = 2y – 6Revised Equation 1
8Use the substitution method EXAMPLE 2Use the substitution methodSTEP 2Substitute 2y – 6 for x in Equation 2 and solve for y.4x + 6y = 4Write Equation 2.4(2y – 6) + 6y = 4Substitute 2y – 6 for x.8y – y = 4Distributive property14y – 24 = 4Simplify.14y = 28Add 24 to each side.y = 2Divide each side by 14.
9Use the substitution method EXAMPLE 2Use the substitution methodSTEP 3Substitute 2 for y in the revised Equation 1 to find the value of x.x = 2y – 6Revised Equation 1x = 2(2) – 6Substitute 2 for y.x = –2Simplify.ANSWERThe solution is (–2, 2).
10Use the substitution method EXAMPLE 2GUIDED PRACTICEUse the substitution methodCHECKSubstitute –2 for x and 2 for y in each of the originalequations.Equation 1Equation 24x + 6y = 4x – 2y = –6–2 – 2(2) = –6?4(–2) + 6 (2) = 4?–6 = –64 = 4
11EXAMPLE 1GUIDED PRACTICEUse the substitution methodfor Examples 1 and 2Solve the linear system using the substitution method.y = 2x + 51.3x + y = 10ANSWER(1, 7)
12EXAMPLE 2GUIDED PRACTICEUse the substitution methodfor Examples 1 and 2Solve the linear system using the substitution method.x – y = 32.x + 2y = –6ANSWER(0, –3)
13EXAMPLE 2GUIDED PRACTICEUse the substitution methodfor Examples 1 and 2Solve the linear system using the substitution method.3x + y = –73.–2x + 4y = 0ANSWER(–2, –1)
14EXAMPLE 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.
15EXAMPLE 3Solve a multi-step problemSOLUTIONSTEP 1Write a system of equations. Let y be the totalcost after x months.Equation 1: Internet service providery = x
16Solve a multi-step problem EXAMPLE 3Solve a multi-step problemEquation 2: Website hosting companyy = xThe system of equations is:y = xEquation 1y = 22.45xEquation 2
17Solve a multi-step problem EXAMPLE 3Solve a multi-step problemSTEP 2Substitute 22.45x for y in Equation 1 and solvefor x.y = xWrite Equation 1.22.45x = xSubstitute 22.45x for y.0.5x = 10Subtract 21.95x from each side.x = 20Divide each side by 0.5.The total cost will be the same for both companies after 20 months.ANSWER