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Rearranging Equations

Rearranging Equations. z. x. 2y. What might this represent?. z. x. 2y. Example: x + z = 2y. z. x. 2y. x = …. z. x. 2y. x = 2y – z. z. x. 2y. y = …. z. x. 2y. x + z 2. y =. 3z =. z =. 2x. 2y. 3z. y =. 2y =. 3z = 2x + 2y. z =. 2x. 2y. 3z. y =. 2y =.

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Rearranging Equations

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  1. Rearranging Equations

  2. z x 2y What might this represent?

  3. z x 2y Example: x + z = 2y

  4. z x 2y x = …

  5. z x 2y x = 2y – z

  6. z x 2y y = …

  7. z x 2y x + z 2 y =

  8. 3z = z = 2x 2y 3z y = 2y =

  9. 3z = 2x + 2y z = 2x 2y 3z y = 2y =

  10. 3z = 2x + 2y z = (2x + 2y) 3 2x 2y 3z y = 2y =

  11. z = (2x + 2y) 3 3z = 2x + 2y 2x 2y 3z y = 2y = 3z – 2x

  12. z = (2x + 2y) 3 3z = 2x + 2y 2x 2y 3z y = (3z – 2x) 2 2y = 3z – 2x

  13. 2y = 3x + 4z Draw this!

  14. 3x – z = 2y Draw this!

  15. 3x – z = 2y Solve for 3x!

  16. 3x – z = 2y Solve for x!

  17. True or False? z = x + 2y + g3 x + 2y = 3z - g

  18. Cheat sheet: How to rearrange equations • Want to get rid of something that is added? Subtract it from both sides. • Want to get rid of something that is subtracted? Add it to both sides. • Want to get rid of something that is multiplied? Divide both sides by it. • 4. Want to get rid of something that is divided? Multiply both sides by it. If A + B = C, then A = C – B If A – B = C, then A = C + B B C If AB = C, then A = A B If = C, then A = CB

  19. Rearranging Equations Activity • In teams of two: • Cut out each of the equations and representative bars. • Glue 4 coloured bar graphs to a sheet of cardstock, leaving space underneath each. • Figure out which equations describe the bar graphs. Glue these underneath the correct graph. • Write one new equation using each each bar graph solving for a different variable.

  20. Solving Equations

  21. Solving Equations A single equation with one variable has just one solution. Example: 2x – 3 = 5 Solution: x = 4

  22. Solving Equations A single equation with two variables has infinite solutions. Example: x – y = 4 Solutions include: x = 5, y = 1 x = 1, y = -3 x = 4, y = 0 etc. We write these solutions as: (5, 1) (1, -3) (4, 0)

  23. Solving Equations A single equation with two variables has infinite solutions. Which of the following is a solution to: 2x – y = 5 • (2, 1) • (2, -1) • (3, 2) • (0, 5)

  24. Solving Equations A single equation with two variables has infinite solutions. Which of the following is a solution to: 2x – y = 5 • (2, 1) • (2, -1) • (3, 2) • (0, 5) 2(2) – (-1) = 5

  25. Solving Equations A system of two equations with two common variables has justone solution. Example: x – y = 4 x + 2y = 13 Check the following solutions. Which works for both equations? A) x = 6, y = 2 B) x = 5, y = 4 C) x = 7, y = 3 D) x = 8, y = 4

  26. Solving Equations A system of two equations with two common variables has justone solution. Example: x – y = 4 x + 2y = 13 Check the following solutions. Which works for both equations? A) x = 6, y = 2 B) x = 5, y = 4 C) x = 7, y = 3 D) x = 8, y = 4 We write this solutions as: (7, 3)

  27. Apply it! The admission fee for Amy’s athletics workshop is 10$ for children and 15$ for adults. Amy makes $235 for her workshop and 18 people attend. A) Set up a system of equations with this information. B) Figure out how many adults and how many children attended.

  28. In your teams A buffet restaurant decides to charge 10$ per meal for children and 16$ per meal for adults. One day, the restaurant has 95 customers and makes $1370. A) Set up a system of equations for this scenario. B) Figure out how many adults and how many children ate at the restaurant.

  29. Homework Academic: Page 4 - 5 1-ordered pairs and one equation #1, 2 2-ordered pairs and two equations #1, 2 3-problem solving #1 Applied: Page 3 #4, 6, 10 If time, check out examples on page 5 – 6, and try page 7 #1 – 3, 13, 14

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