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**Solving Systems of Equations**

Today’s Lesson Solving Systems of Equations

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Warm-Up Activity We will warm up today by working with equations.

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**5x + 7 = 32 5(5) + 7 = 32 25 + 7 = 32 32 = 32 Solve the equation.**

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

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**Solve and check your work using substitution.**

3x – 7 = 14 x = 7 3(7) – 7 = 14 21 – 7 = 14 14 = 14

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**Solve and check your work using substitution.**

x + 3 = –15 x = 27 (27) + 3 = –15 – = –15 –15 = –15

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**Solve and check your work using substitution.**

x – 8= 36 x = 176 (176) – 8 = 36 44 – 8 = 36 36 = 36

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**Whole-Class Skills Lesson**

Today, you will solve systems of two linear equations with two variables using the substitution method.

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Kimo and Sadi had a total of 8 wooden cars. Each of Kimo’s cars cost $2. Each of Sadi’s 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? two equations x = the number of Kimo’s cars y = the number of Sadi’s cars

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**x + y = 8 Write an equation for the total number of cars.**

Kimo and Sadi had a total of 8 wooden cars. Each of Kimo’s cars cost $2. Each of Sadi’s 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 Kimo’s cars y = the number of Sadi’s cars Write an equation for the total number of cars. x + y = 8

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Kimo and Sadi had a total of 8 wooden cars. Each of Kimo’s cars cost $2. Each of Sadi’s 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 Kimo’s cars y = the number of Sadi’s cars Write an equation for the amount of money spent for all the cars. 2x + 3y = 19

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x + y = 8 y x y 2 3 4 5 6 5 4 3 x Sub in for x to find y.

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**2x + 3y = 19 4.33 3.66 3 2.33 Sub in for x to find y. x y 3 4 5 6 y**

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**Where do the lines intersect?**

y x + y = 8 (5, 3) 2x + 3y = 19 2 1 x 1 2

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**What does the point, (5, 3) represent?**

x = the number of Kimo’s cars y = the number of Sadi’s cars y x + y = 8 What does the point, (5, 3) represent? (5, 3) 2x + 3y = 19 x = y = 3 Kimo has 5 cars. Sadi has 3 cars. 2 1 x 1 2

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**Solve the system of equation without graphing**

Solve the system of equation without graphing. Remember you can use substitution. x + y = 8 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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**Use inverse operations to get the x by itself.**

Subtract y from both sides of the first equation. x + y = 8 x + y – y = – y + 8 x = – y + 8

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**2x + 3y = 19 2(– y + 8) + 3y = 19 – 2y + 16 + 3y = 19 y = 3**

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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y = 3 x = – (3) + 8 x = 5 (5 , 3)

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**x + y = 64 Write an equation for the total number of cards.**

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 Chad’s cards y = the number of Craig’s cards Write an equation for the total number of cards. x + y = 64

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**Chad and Craig have 64 baseball card all together**

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 Chad’s cards y = the number of Craig’s cards Write an equation for the amount of money spent for all the cards. 4x + 2y = 184

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**Solve the system by using substitution.**

x + y = 64 x = – y + 64 4x + 2y = 184 4(– y + 64) + 2y = 184 – 2y = – 72 y = 36

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**If y = 36 then sub in to find x.**

x + y = 64 x + 36 = 64 x = 28 (28, 36)

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**Chad has 28 baseball cards and Craig has 36 baseball cards.**

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 Chad’s cards y = the number of Craig’s cards (28, 36) Chad has 28 baseball cards and Craig has 36 baseball cards.

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