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Solving Systems of Equations

Today’s Lesson. Solving Systems of Equations. Warm-Up Activity. We will warm up today by working with equations. Solve the equation. 5 x + 7 = 32. – 7 – 7. 5 x = 25. ÷ 5 ÷ 5. x = 5.

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Solving Systems of Equations

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  1. Today’s Lesson Solving Systems of Equations

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

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

  4. Solve and check your work using substitution. 3x – 7 = 14 x = 7 3(7) – 7 = 14 21 – 7 = 14 14 = 14

  5. Solve and check your work using substitution. x + 3 = –15 x = 27 (27) + 3 = –15 – 18 + 3 = –15 –15 = –15

  6. Solve and check your work using substitution. x – 8= 36 x = 176 (176) –8 = 36 44 – 8 = 36 36 = 36

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

  8. 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

  9. 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

  10. 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

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

  12. 2x + 3y = 19 y x + y = 8 4.33 2x + 3y = 19 3.66 2 3 1 2.33 x 1 2 Sub in for x to find y.

  13. Where do the lines intersect? y x + y = 8 (5, 3) 2x +3y = 19 2 1 x 1 2

  14. 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 = 5 y = 3 Kimo has 5 cars. Sadi has 3 cars. 2 1 x 1 2

  15. 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.

  16. 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

  17. Substitute the new equation in for x. x = – y + 8 2x + 3y = 19 2(– y + 8) + 3y =19 – 2y + 16 + 3y =19 y =3

  18. y =3 x = – (3)+ 8 x =5 (5 , 3)

  19. 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

  20. 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

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

  22. If y = 36 then sub in to find x. x + y = 64 x + 36= 64 x = 28 (28, 36)

  23. 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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