Algebra 1 Notes Lesson 7-3 Elimination Using Addition and Subtraction

1. Algebra 1 Notes Lesson 7-3 Elimination Using Addition and Subtraction

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3. Mathematics Standards • 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. • 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. Vocabulary • Elimination – Third method to solve system of equations. Add or subtract equations. • First was Graphing. • Second was Substitution.

5. Example 1 Use elimination to solve the system of equations. -3x + 4y = 12 3x – 6y = 18

6. Example 1 Use elimination to solve the system of equations. -3x + 4y = 12 3x – 6y = 18

7. Example 1 Use elimination to solve the system of equations. -3x + 4y = 12 (+)3x – 6y = 18 -2y =

8. Example 1 Use elimination to solve the system of equations. -3x + 4y = 12 (+)3x – 6y = 18 -2y = 30 -2 -2 y = -15

9. Example 1 Use elimination to solve the system of equations. -3x + 4y = 12 (+) 3x – 6y = 18 -2y = 30 -2 -2 y = -15

10. Example 1 Use elimination to solve the system of equations. -3x + 4y = 12 -3x + 4(-15) = 12 (+) 3x – 6y = 18 -2y = 30 -2 -2 y = -15

11. Example 1 Use elimination to solve the system of equations. -3x + 4y = 12 -3x + 4(-15) = 12 (+) 3x – 6y = 18 -3x – 60 = 12 -2y = 30 -2 -2 y = -15

12. Example 1 Use elimination to solve the system of equations. -3x + 4y = 12 -3x + 4(-15) = 12 (+) 3x – 6y = 18 -3x – 60 = 12 -2y = 30 +60 +60 -2 -2 y = -15

13. Example 1 Use elimination to solve the system of equations. -3x + 4y = 12 -3x + 4(-15) = 12 (+) 3x – 6y = 18 -3x – 60 = 12 -2y = 30 +60 +60 -2 -2 -3x = 72 y = -15

14. Example 1 Use elimination to solve the system of equations. -3x + 4y = 12 -3x + 4(-15) = 12 (+) 3x – 6y = 18 -3x – 60 = 12 -2y = 30 +60 +60 -2 -2 -3x = 72 y = -15 -3 -3

15. Example 1 Use elimination to solve the system of equations. -3x + 4y = 12 -3x + 4(-15) = 12 (+) 3x – 6y = 18 -3x – 60 = 12 -2y = 30 +60 +60 -2 -2 -3x = 72 y = -15 x = -24 -3 -3

16. Example 1 Use elimination to solve the system of equations. -3x + 4y = 12 -3x + 4(-15) = 12 (+) 3x – 6y = 18 -3x – 60 = 12 -2y = 30 +60 +60 -2 -2 (-24, -15) -3x = 72 y = -15 x = -24 -3 -3

17. Example 2 Use elimination to solve the system of equations. 4x + 2y = 28 4x – 3y = 18

18. Example 2 Use elimination to solve the system of equations. 4x + 2y = 28 4x – 3y = 18

19. Example 2 Use elimination to solve the system of equations. 4x + 2y = 28 (–)4x – 3y = 18 5y =

20. Example 2 Use elimination to solve the system of equations. 4x + 2y = 28 (–)4x – 3y = 18 5y = 10

21. Example 2 Use elimination to solve the system of equations. 4x + 2y = 28 (–) 4x – 3y = 18 5y = 10 5 5 y = 2

22. Example 2 Use elimination to solve the system of equations. 4x + 2y = 28 (–) 4x – 3y = 18 5y = 10 5 5 y = 2

23. Example 2 Use elimination to solve the system of equations. 4x + 2y = 28 4x + 2(2) = 28 (–) 4x – 3y = 18 5y = 10 5 5 y = 2

24. Example 2 Use elimination to solve the system of equations. 4x + 2y = 28 4x + 2(2) = 28 (–) 4x – 3y = 18 4x + 4 = 28 5y = 10 5 5 y = 2

25. Example 2 Use elimination to solve the system of equations. 4x + 2y = 28 4x + 2(2) = 28 (–) 4x – 3y = 18 4x + 4 = 28 5y = 10 – 4 – 4 5 5 y = 2

26. Example 2 Use elimination to solve the system of equations. 4x + 2y = 28 4x + 2(2) = 28 (–) 4x – 3y = 18 4x + 4 = 28 5y = 10 – 4 – 4 5 5 4x = 24 y = 2

27. Example 2 Use elimination to solve the system of equations. 4x + 2y = 28 4x + 2(2) = 28 (–) 4x – 3y = 18 4x + 4 = 28 5y = 10 – 4 – 4 5 5 4x = 24 y = 2 4 4 x = 6

28. Example 2 Use elimination to solve the system of equations. 4x + 2y = 28 4x + 2(2) = 28 (–) 4x – 3y = 18 4x + 4 = 28 5y = 10 – 4 – 4 5 5 4x = 24 y = 2 4 4 (6, 2)x = 6

29. Example 3 Four times one number minus three times another number is 12. Two times the first number added to three times the second number is 6. Find the numbers. 4n

30. Example 3 Four times one number minus three times another number is 12. Two times the first number added to three times the second number is 6. Find the numbers. 4n – 3m

31. Example 3 Four times one number minus three times another number is 12. Two times the first number added to three times the second number is 6. Find the numbers. 4n – 3m = 12 2n

32. Example 3 Four times one number minus three times another number is 12. Two times the first number added to three times the second number is 6. Find the numbers. 4n – 3m = 12 2n + 3m

33. Example 3 Four times one number minus three times another number is 12. Two times the first number added to three times the second number is 6. Find the numbers. 4n – 3m = 12 2n + 3m = 6

34. Example 3 Four times one number minus three times another number is 12. Two times the first number added to three times the second number is 6. Find the numbers. 4n – 3m = 12 2n + 3m = 6

35. Example 3 Four times one number minus three times another number is 12. Two times the first number added to three times the second number is 6. Find the numbers. 4n – 3m = 12 (+) 2n + 3m = 6 6n = 18 6 6 n = 3

36. Example 3 Four times one number minus three times another number is 12. Two times the first number added to three times the second number is 6. Find the numbers. 4n – 3m = 12 (+) 2n + 3m = 6 6n = 18 6 6 n = 3

37. Example 3 Four times one number minus three times another number is 12. Two times the first number added to three times the second number is 6. Find the numbers. 4n – 3m = 12 4(3) – 3m = 12 (+) 2n + 3m = 6 6n = 18 6 6 n = 3

38. Example 3 Four times one number minus three times another number is 12. Two times the first number added to three times the second number is 6. Find the numbers. 4n – 3m = 12 4(3) – 3m = 12 (+) 2n + 3m = 6 12 – 3m = 12 6n = 18 6 6 n = 3

39. Example 3 Four times one number minus three times another number is 12. Two times the first number added to three times the second number is 6. Find the numbers. 4n – 3m = 12 4(3) – 3m = 12 (+) 2n + 3m = 6 12 – 3m = 12 6n = 18 – 12 – 12 6 6 n = 3

40. Example 3 Four times one number minus three times another number is 12. Two times the first number added to three times the second number is 6. Find the numbers. 4n – 3m = 12 4(3) – 3m = 12 (+) 2n + 3m = 6 12 – 3m = 12 6n = 18 – 12 – 12 6 6 -3m = 0 n = 3

41. Example 3 Four times one number minus three times another number is 12. Two times the first number added to three times the second number is 6. Find the numbers. 4n – 3m = 12 4(3) – 3m = 12 (+) 2n + 3m = 6 12 – 3m = 12 6n = 18 – 12 – 12 6 6 -3m = 0 n = 3 m = 0

42. Example 3 Four times one number minus three times another number is 12. Two times the first number added to three times the second number is 6. Find the numbers. 4n – 3m = 12 4(3) – 3m = 12 (+) 2n + 3m = 6 12 – 3m = 12 6n = 18 – 12 – 12 6 6 -3m = 0 n = 3 3 and 0m = 0

43. Example 4 2x + 3y = 7 7x + 2y = 32

44. Example 4 2x + 3y = 7 7x + 2y = 32 Uh Oh……

45. Example 4 2x + 3y = 7 7x + 2y = 32 Uh Oh…… We will learn how to solve these in the next section.

46. Homework Pg. 385 12-32 (evens) 34,35, and 40