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 24x + 2y = 46 3x + 2y = 37

7. Example 1 Use elimination to solve the system of equations. 2x +y = 23 multiply by 24x + 2y = 46 3x + 2y = 37 keep the same

8. Example 1 Use elimination to solve the system of equations. 2x +y = 23 multiply by 24x + 2y = 46 3x + 2y = 37 3x + 2y = 37

9. Example 1 Use elimination to solve the system of equations. 2x +y = 23 multiply by 24x + 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 24x + 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 24x + 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 24x + 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 24x + 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 24x + 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 24x + 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 24x + 2y = 46 3x + 2y = 37 (–)3x + 2y = 37 3(9) + 2y = 37 x = 9 27 + 2y = 37 – 27 – 27 2y = 10 2 2y = 5

17. Example 1 Use elimination to solve the system of equations. 2x +y = 23 multiply by 24x + 2y = 46 3x + 2y = 37 (–)3x + 2y = 37 3(9) + 2y = 37 x = 9 27 + 2y = 37 – 27 – 27 (9, 5) 2y = 10 2 2y = 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 = 8multiply by 3 3x – 5y = -23

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

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

22. Example 2 Use elimination to solve the system of equations. 4x + 3y = 8multiply by 3 12x + 9y = 24 3x – 5y = -23 multiply by 412x – 20y = -92

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

29. Example 2 Use elimination to solve the system of equations. 4x + 3y = 8multiply 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 3x = -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 = 43x – 7y = -10 – 5y – 5y x = 4 – 5y

34. Example 3 x + 5y = 43x – 7y = -10 – 5y – 5y x = 4 – 5y

35. Example 3 x + 5y = 43x – 7y = -10 – 5y – 5y 3(4 – 5y) – 7y = -10 x = 4 – 5y

36. Example 3 x + 5y = 43x – 7y = -10 – 5y – 5y 3(4 – 5y) – 7y = -10 x = 4 – 5y

37. Example 3 x + 5y = 43x – 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

38. Example 3 x + 5y = 43x – 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 = 43x – 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 = 43x – 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 = 43x – 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 = 43x – 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