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© Teacher Created Materials Solving Systems of Equations Todays Lesson

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© Teacher Created Materials Warm-Up Activity We will warm up today by working with equations.

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© Teacher Created Materials 5x + 7 = 32 – 7 5x = 25 ÷ 5 x = 5 Solve the equation. Check your answer using substitution. If the left and right side match, you have the correct answer. 5(5) + 7 = = = 32

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© Teacher Created Materials Solve and check your work using substitution. 3x – 7 = 14 x = 7 3(7) – 7 = – 7 = = 14

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© Teacher Created Materials Solve and check your work using substitution. x + 3 = –15 x = 27 (27) + 3 = –15 – = –15 –15 = –15

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© Teacher Created Materials Solve and check your work using substitution. x – 8= 36 x = 176 (176) – 8 = – 8 = = 36

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© Teacher Created Materials Today, you will solve systems of two linear equations with two variables using the substitution method. Whole-Class Skills Lesson

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© Teacher Created Materials Kimo and Sadi had a total of 8 wooden cars. Each of Kimos cars cost $2. Each of Sadis cars cost $3. Kimo and Sadi spent a total of $19. How many cars does Kimo have? How many cars does Sadi have? How many equations can be written from the information in the problem? x = the number of Kimos cars y = the number of Sadis cars two equations

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© Teacher Created Materials Write an equation for the total number of cars. x + y = 8 Kimo and Sadi had a total of 8 wooden cars. Each of Kimos cars cost $2. Each of Sadis cars cost $3. Kimo and Sadi spent a total of $19. How many cars does Kimo have? How many cars does Sadi have? x = the number of Kimos cars y = the number of Sadis cars

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© Teacher Created Materials Write an equation for the amount of money spent for all the cars. 2x + 3y = 19 Kimo and Sadi had a total of 8 wooden cars. Each of Kimos cars cost $2. Each of Sadis cars cost $3. Kimo and Sadi spent a total of $19. How many cars does Kimo have? How many cars does Sadi have? x = the number of Kimos cars y = the number of Sadis cars

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© Teacher Created Materials x + y = 8 Sub in for x to find y. xy x y

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© Teacher Created Materials 2x + 3y = 19 Sub in for x to find y. xy x y x + y = x + 3y = 19

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© Teacher Created Materials Where do the lines intersect? x y x + y = x + 3y = 19 (5, 3)

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© Teacher Created Materials What does the point, (5, 3) represent? x y x + y = x + 3y = 19 (5, 3) x = 5 y = 3 Kimo has 5 cars. Sadi has 3 cars. x = the number of Kimos cars y = the number of Sadis cars

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© Teacher Created Materials x + y = 8 Solve the system of equation without graphing. Remember you can use substitution. 2x + 3y = 19 We can rewrite the first equation so x is by itself on the left side of the equation.

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© Teacher Created Materials x + y – y = – y + 8 Use inverse operations to get the x by itself. Subtract y from both sides of the first equation. x = – y + 8 x + y = 8

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© Teacher Created Materials Substitute the new equation in for x. x = – y + 8 2x + 3y = 19 2(– y + 8) + 3y = 19 – 2y y = 19 y = 3

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© Teacher Created Materials x = – (3) + 8 y = 3 x = 5 (5, 3)

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© Teacher Created Materials Write an equation for the total number of cards. x + y = 64 Chad and Craig have 64 baseball card all together. Chad paid 4 dollars for each of his cards, and Craig paid 2 dollars for each of his card. How many baseball cards do each of the boys have? x = the number of Chads cards y = the number of Craigs cards

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© Teacher Created Materials Write an equation for the amount of money spent for all the cards. 4x + 2y = 184 Chad and Craig have 64 baseball card all together. Chad paid 4 dollars for each of his cards, and Craig paid 2 dollars for each of his card. Together they have spent a total of $184. How many baseball cards do each of the boys have? x = the number of Chads cards y = the number of Craigs cards

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© Teacher Created Materials x + y = 64 4(– y + 64) + 2y = 184 Solve the system by using substitution. x = – y x + 2y = 184 – 2y = – 72 y = 36

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© Teacher Created Materials x + y = 64 If y = 36 then sub in to find x. x + 36 = 64 x = 28 (28, 36)

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© Teacher Created Materials Chad and Craig have 64 baseball card all together. Chad paid 4 dollars for each of his cards, and Craig paid 2 dollars for each of his card. How many baseball cards do each of the boys have? x = the number of Chads cards y = the number of Craigs cards (28, 36) Chad has 28 baseball cards and Craig has 36 baseball cards.

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