1. Systems of Linear Equations Block 44

2. System of Linear Equations A system of equations is a set or collection of equations that you deal with all together at once. Linear equations (ones that graph as straight lines) are simpler than non- linear equations The simplest linear system is one with two equations and two variables.

3. Graph of a Linear Equation Graph of y = 3x – 2 xy 11 0-2 -5

4. Graph of a Linear Equation Graph of y = –x – 6 xy 1-7 0-6 -5

5. System of Linear Equations Graph of y = 3x – 2 & y = –x – 6 xy 11 0-2 -5 xy 1-7 0-6 -5

6. System of Linear Equations Graph of y = 3x – 2 & y = –x – 6 xy 11 0-2 -5 xy 1-7 0-6 -5 Solution is (-1, -5)

7. Practice Solving Systems of Linear Equations Solve by Graphing the following systems of linear equations (see worksheet #1): #1

8. Practice Solving Systems of Linear Equations Solve by Graphing the following systems of linear equations (see worksheet #1): #2

9. Practice Solving Systems of Linear Equations Solve by Graphing the following systems of linear equations (see worksheet #1): #3

10. Practice Solving Systems of Linear Equations Solve by Graphing the following systems of linear equations (see worksheet #1): #4

11. Practice Solving Systems of Linear Equations Solve by Graphing the following systems of linear equations (see worksheet #1): #5

12. Solving Systems of Linear Equations Substitution Method: 2x – 3y = –2 4x + y = 24 Choose 2 nd equation: 4x + y = 24 Rewrite with single variable: y = 24 – 4x Substitute into 1 st equation: 2x – 3(24 – 4x) = –2

13. Solving Systems of Linear Equations Substitution Method: 2x – 3y = –2 4x + y = 24 Simplify: 2x – 72 + 12x = –2 14x – 72 = -2 14x = 70 x = 5

14. Solving Systems of Linear Equations Substitution Method: 2x – 3y = –2 4x + y = 24 Substitute x = 5 into either equation: 4x + y = 24 4(5) + y = 24 20 + y = 24 y = 24 – 20 y = 4

15. Solving Systems of Linear Equations Substitution Method: 2x – 3y = –2 4x + y = 24 The solution is the ordered pair (5, 4).

16. Practice Solving Systems of Linear Equations Solve by Substitution the following systems of linear equations (see worksheet #2): #1

17. Practice Solving Systems of Linear Equations Solve by Substitution the following systems of linear equations (see worksheet #2): #2

18. Practice Solving Systems of Linear Equations Solve by Substitution the following systems of linear equations (see worksheet #2): #3

19. Practice Solving Systems of Linear Equations Solve by Substitution the following systems of linear equations (see worksheet #2): #4

20. Practice Solving Systems of Linear Equations Solve by Substitution the following systems of linear equations (see worksheet #2): #5

21. Solving an Equation Addition or Elimination Method: Example: x + 6 = 11 -6 -6 x = 5

22. Solving Systems of Linear Equations Addition or Elimination Method-easy: 2x + y = 9 3x – y = 16 Add: 5x = 25 Simplify: x = 5 Substitute: 2(5) + y = 9 10 + y = 9 y = -1

23. Solving Systems of Linear Equations Addition or Elimination Method - easy: 2x + y = 9 3x – y = 16 Solution is (5, -1)

24. Solving Systems of Linear Equations Addition or Elimination Method – medium: 2x – y = 9 3x + 4y = –14 Multiply 1 st by 4: 8x – 4y = 36 8x – 4 y = 36 3x + 4y = –14

25. Solving Systems of Linear Equations Addition or Elimination Method – medium: 8x – 4 y = 36 3x + 4y = –14 Multiply 1 st by 4: 8x – 4y = 36 Add: 11x = 22 Simplify: x = 2 Substitute: 2(2) – y = 9 4 – y = 9 -y = 5 or y = -5

26. Solving Systems of Linear Equations Addition or Elimination Method – medium: 2x – y = 9 3x + 4y = –14 Solution is (2, -5)

27. Solving Systems of Linear Equations Addition or Elimination Method – hard: 4x – 3y = 25 –3x + 8y = 10 Multiply 1 st by 3: 12x – 9y = 75 Multiply 2 nd by 4: -12x + 32y = 40

28. Solving Systems of Linear Equations Addition or Elimination Method – hard: 12x – 9y = 75 -12x + 32y = 40 Add: 23y = 115 Simplify: y = 5 Substitute (original equation) : 4x – 3y = 25 4x – 3(5) = 25 4x = 40 x = 10 Solution is (10, 5)

29. Practice Solving Systems of Linear Equations Solve by Addition/Elimination the following systems of linear equations (see worksheet #3): #1

30. Practice Solving Systems of Linear Equations Solve by Addition/Elimination the following systems of linear equations (see worksheet #3): #2

31. Practice Solving Systems of Linear Equations Solve by Addition/Elimination the following systems of linear equations (see worksheet #3): #3

32. Practice Solving Systems of Linear Equations Solve by Addition/Elimination the following systems of linear equations (see worksheet #3): #4

33. Practice Solving Systems of Linear Equations Solve by Addition/Elimination the following systems of linear equations (see worksheet #3): #5