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Algebra 1 Notes Lesson 7-4 Elimination Using Multiplication

Algebra 1 Notes Lesson 7-4 Elimination Using Multiplication. Mathematics Standards Number, Number Sense and Operations : Explain the effects of operations such as multiplication or division, and of computing the powers and roots on the magnitude of quantities.

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Algebra 1 Notes Lesson 7-4 Elimination Using Multiplication

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  1. Algebra 1 Notes Lesson 7-4 Elimination Using Multiplication

  2. Mathematics Standards • Number, Number Sense and Operations: Explain the effects of operations such as multiplication or division, and of computing the powers and roots on the magnitude of quantities. • Patterns, Functions and Algebra: Add, subtract, multiply and divide monomials and polynomials. • Patterns, Functions and Algebra: Solve real-world problems that can be modeled using linear, quadratic, exponential or square root functions.

  3. Mathematics Standards • Patterns, Functions and Algebra: Solve and interpret the meaning of 2 by 2 systems of linear equations graphically, by substitution and by elimination, with and without technology. • Patterns, Functions and Algebra: Solve real world problems that can be modeled using systems of linear equations and inequalities.

  4. Elimination with Multiplication One more step than before

  5. Example 1 Use elimination to solve the system of equations. 2x +y = 23 3x + 2y = 37 multiply by 2

  6. Example 1 Use elimination to solve the system of equations. 2x +y = 23 multiply by 2 4x + 2y = 46 3x + 2y = 37

  7. Example 1 Use elimination to solve the system of equations. 2x +y = 23 multiply by 2 4x + 2y = 46 3x + 2y = 37 keep the same

  8. Example 1 Use elimination to solve the system of equations. 2x +y = 23 multiply by 2 4x + 2y = 46 3x + 2y = 37 3x + 2y = 37

  9. Example 1 Use elimination to solve the system of equations. 2x +y = 23 multiply by 2 4x + 2y = 46 3x + 2y = 37 (–) 3x + 2y = 37 x = 9

  10. Example 1 Use elimination to solve the system of equations. 2x +y = 23 multiply by 2 4x + 2y = 46 3x + 2y = 37 (–) 3x + 2y = 37 x = 9

  11. Example 1 Use elimination to solve the system of equations. 2x +y = 23 multiply by 2 4x + 2y = 46 3x + 2y = 37 (–) 3x + 2y = 37 3(9) + 2y = 37 x = 9 .

  12. Example 1 Use elimination to solve the system of equations. 2x +y = 23 multiply by 2 4x + 2y = 46 3x + 2y = 37 (–) 3x + 2y = 37 3(9) + 2y = 37 x = 9 27 + 2y = 37

  13. Example 1 Use elimination to solve the system of equations. 2x +y = 23 multiply by 2 4x + 2y = 46 3x + 2y = 37 (–) 3x + 2y = 37 3(9) + 2y = 37 x = 9 27 + 2y = 37 – 27 – 27

  14. Example 1 Use elimination to solve the system of equations. 2x +y = 23 multiply by 2 4x + 2y = 46 3x + 2y = 37 (–) 3x + 2y = 37 3(9) + 2y = 37 x = 9 . 27 + 2y = 37 – 27 – 27 2y = 10

  15. Example 1 Use elimination to solve the system of equations. 2x +y = 23 multiply by 2 4x + 2y = 46 3x + 2y = 37 (–) 3x + 2y = 37 3(9) + 2y = 37 x = 9 27 + 2y = 37 – 27 – 27 2y = 10 2 2

  16. Example 1 Use elimination to solve the system of equations. 2x +y = 23 multiply by 2 4x + 2y = 46 3x + 2y = 37 (–) 3x + 2y = 37 3(9) + 2y = 37 x = 9 27 + 2y = 37 – 27 – 27 2y = 10 2 2 y = 5

  17. Example 1 Use elimination to solve the system of equations. 2x +y = 23 multiply by 2 4x + 2y = 46 3x + 2y = 37 (–) 3x + 2y = 37 3(9) + 2y = 37 x = 9 27 + 2y = 37 – 27 – 27 (9, 5) 2y = 10 2 2 y = 5

  18. Example 2 Use elimination to solve the system of equations. 4x + 3y = 8 3x – 5y = -23

  19. Example 2 Use elimination to solve the system of equations. 4x + 3y = 8 multiply by 3 3x – 5y = -23

  20. Example 2 Use elimination to solve the system of equations. 4x + 3y = 8 multiply by 3 12x + 9y = 24 3x – 5y = -23

  21. Example 2 Use elimination to solve the system of equations. 4x + 3y = 8 multiply by 3 12x + 9y = 24 3x – 5y = -23 multiply by 4

  22. Example 2 Use elimination to solve the system of equations. 4x + 3y = 8 multiply by 3 12x + 9y = 24 3x – 5y = -23 multiply by 4 12x – 20y = -92

  23. Example 2 Use elimination to solve the system of equations. 4x + 3y = 8 multiply by 3 12x + 9y = 24 3x – 5y = -23 multiply by 4 (-)12x – 20y = -92 29y = 116 29 29 y = 4

  24. Example 2 Use elimination to solve the system of equations. 4x + 3y = 8 multiply by 3 12x + 9y = 24 3x – 5y = -23 multiply by 4(-)12x – 20y = -92 29y = 116 29 29 y = 4

  25. Example 2 Use elimination to solve the system of equations. 4x + 3y = 8 multiply by 3 12x + 9y = 24 3x – 5y = -23 multiply by 4(-)12x – 20y = -92 3x – 5(4) = -23 29y = 116 29 29 y = 4

  26. Example 2 Use elimination to solve the system of equations. 4x + 3y = 8 multiply by 3 12x + 9y = 24 3x – 5y = -23 multiply by 4(-)12x – 20y = -92 3x – 5(4) = -23 29y = 116 3x – 20 = -23 29 29 y = 4

  27. Example 2 Use elimination to solve the system of equations. 4x + 3y = 8 multiply by 3 12x + 9y = 24 3x – 5y = -23 multiply by 4 (-)12x – 20y = -92 3x – 5(4) = -23 29y = 116 3x – 20 = -23 29 29 +20 +20 y = 4 3x = -3 3 3

  28. Example 2 Use elimination to solve the system of equations. 4x + 3y = 8 multiply by 3 12x + 9y = 24 3x – 5y = -23 multiply by 4 (-)12x – 20y = -92 3x – 5(4) = -23 29y = 116 3x – 20 = -23 29 29 +20 +20 y = 4 3x = -3 3 3 x = -1

  29. Example 2 Use elimination to solve the system of equations. 4x + 3y = 8 multiply by 3 12x + 9y = 24 3x – 5y = -23 multiply by 4 (-)12x – 20y = -92 3x – 5(4) = -23 29y = 116 3x – 20 = -23 29 29 +20 +20 y = 4 3x = -3 3 3 x = -1 (-1, 4)

  30. Example 3 Determine the best method to solve the system of equations. Then solve the system. x + 5y = 4 3x – 7y = -10

  31. Example 3 Three Options: Graphing – Rarely best Substitution – If variable is solved for or easily solved for Elimination – If variable has same coefficient or solving for a variable gives a fraction

  32. Example 3 Determine the best method to solve the system of equations. Then solve the system. x + 5y = 4 3x – 7y = -10 The best method to use is substitution because the coefficient of x in the first equation is 1, which makes it easy to solve for.

  33. Example 3 x + 5y = 4 3x – 7y = -10 – 5y – 5y x = 4 – 5y

  34. Example 3 x + 5y = 4 3x – 7y = -10 – 5y – 5y x = 4 – 5y

  35. Example 3 x + 5y = 4 3x – 7y = -10 – 5y – 5y 3(4 – 5y) – 7y = -10 x = 4 – 5y

  36. Example 3 x + 5y = 4 3x – 7y = -10 – 5y – 5y 3(4 – 5y) – 7y = -10 x = 4 – 5y

  37. Example 3 x + 5y = 4 3x – 7y = -10 – 5y – 5y 3(4 – 5y) – 7y = -10 x = 4 – 5y 12 – 15y – 7y = -10 12 – 22y = -10 – 12 – 12 -22y = -22 -22 -22 y = 1

  38. Example 3 x + 5y = 4 3x – 7y = -10 – 5y – 5y 3(4 – 5y) – 7y = -10 x = 4 – 5y12 – 15y – 7y = -10 12 – 22y = -10 – 12 – 12 -22y = -22 -22 -22 y = 1

  39. Example 3 x + 5y = 4 3x – 7y = -10 – 5y – 5y 3(4 – 5y) – 7y = -10 x = 4 – 5y12 – 15y – 7y = -10 x = 4 – 5(1) 12 – 22y = -10 – 12 – 12 -22y = -22 -22 -22 y = 1

  40. Example 3 x + 5y = 4 3x – 7y = -10 – 5y – 5y 3(4 – 5y) – 7y = -10 x = 4 – 5y12 – 15y – 7y = -10 x = 4 – 5(1) 12 – 22y = -10 x = 4 – 5 – 12 – 12 -22y = -22 -22 -22 y = 1

  41. Example 3 x + 5y = 4 3x – 7y = -10 – 5y – 5y 3(4 – 5y) – 7y = -10 x = 4 – 5y12 – 15y – 7y = -10 x = 4 – 5(1) 12 – 22y = -10 x = 4 – 5 – 12 – 12 x = -1 -22y = -22 -22 -22 y = 1

  42. Example 3 x + 5y = 4 3x – 7y = -10 – 5y – 5y 3(4 – 5y) – 7y = -10 x = 4 – 5y12 – 15y – 7y = -10 x = 4 – 5(1) 12 – 22y = -10 x = 4 – 5 – 12 – 12 x = -1 -22y = -22 (-1, 1) -22 -22 y = 1

  43. Homework Pg. 391 14-38 evens

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