3. Graphing Systems 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 Substitution Method Elimination Method Applications Misc.

4. Question: Solve the system graphed. Check Your Answer Graphing for 1

5. Answer: (2, 3) Back to the Game Board Graphing for 1

6. Question: If the equations of a system are graphed to be parallel lines, what is the solution? Check Your Answer Graphing for 2

7. Answer: no solution Back to the Game Board Graphing for 2

8. Question: If a system has infinitely many solutions, what occurs when solving using the graphing method? Check Your Answer Graphing for 3

9. Answer: You get coinciding lines. Back to the Game Board Graphing for 3

10. Question: Solve by graphing. x + y = -1 y = 4x + 4 Check Your Answer Graphing for 4

11. Answer: (-1, 0) Back to the Game Board Graphing for 4

12. Question: State the system shown. Check Your Answer Graphing for 5

13. Answer: y = 2x - 3 y = -x + 4 Back to the Game Board Graphing for 5

14. Question: When is it best to use the substitution method when solving systems? Check Your Answer Substitution for 1

15. Answer: When one of the equations is solved for one variable. Back to the Game Board Substitution for 1

16. Question: Solve by substitution. y = 2x – 3 y = 6 – x Check Your Answer Substitution for 2

17. Answer: (3, 3) Back to the Game Board Substitution for 2

18. Check Your Answer Substitution for 3 Question: Solve by substitution. x = 3y + 5 2x + y = 3

19. Answer: (2, -1) Back to the Game Board Substitution for 3

20. Check Your Answer Substitution for 4 Question: Solve by substitution. 5x – y = 2 y = 5x + 3

21. Answer: no solution Back to the Game Board Substitution for 4

22. Check Your Answer Substitution for 5 Question: Solve by substitution. 3x – y = 11 y = 4x – 15

23. Answer: (4, 1) Back to the Game Board Substitution for 5

24. Question: When is it best to use the elimination method for solving systems? Check Your Answer Elimination for 1

25. Answer: When both equations are in standard form. Back to the Game Board Elimination for 1

26. Question: Solve by elimination. x – 2y = 5 3y + 2y = –1 Check Your Answer Elimination for 2

27. Answer: (1, -2) Back to the Game Board Elimination for 2

28. Question: Solve by elimination. 3x – 5y = 0 –x + 2y = 2 Check Your Answer Elimination for 3

29. Answer: (10, 6) Back to the Game Board Elimination for 3

30. Question: Solve by elimination. 2x – 3y = –1 –6x + 9y = 3 Check Your Answer Elimination for 4

31. Answer: infinitely many solutions Back to the Game Board Elimination for 4

32. Question: Solve by elimination. 4x + 3y = –18 5x – 2y = –11 Check Your Answer Elimination for 5

33. Answer: (-3, -2) Back to the Game Board Elimination for 5

34. Question: Solve by graphing. y > x – 3 y < 5 – x Check Your Answer Inequalities for 1

35. Answer: Back to the Game Board Inequalities for 1

36. Question: Solve by graphing. y ≥ x x < 3 Check Your Answer Inequalities for 2

37. Answer: Back to the Game Board Inequalities for 2

38. Check Your Answer Inequalities for 3 Question: Solve by graphing. 2x – 3y > 12 y > (-1/2)x – 3

39. Answer: Back to the Game Board Inequalities for 3

40. Question: Is (3, -5) a solution to: y > 2 – 7x 2x – 3y < 9 Check Your Answer Inequalities for 4

41. Answer: No; it fails the second inequality. Back to the Game Board Inequalities for 4

42. Question: State the system shown. Check Your Answer Inequalities for 5

43. Answer: y ≥ –2 y < x – 1 Back to the Game Board Inequalities for 5

44. Question: Solve for x. 3x – 7y = 12 2x + 2y = 5 Check Your Answer Miscellaneous for 1

45. Answer: x = 59/20 Back to the Game Board Miscellaneous for 1

46. Question: Solve by graphing. y = 3x + 2 6x – 2y = –4 Check Your Answer Miscellaneous for 2

47. Answer: infinitely many solutions (the lines are coinciding) Back to the Game Board Miscellaneous for 2

48. Question: Two numbers add to 9. One is 5 more than the other. What are the numbers? Check Your Answer Miscellaneous for 3

49. Answer: 7 and 2 x + y = 9 x = y + 5 Back to the Game Board Miscellaneous for 3

50. Check Your Answer Miscellaneous for 4 Question: You buy 25 CD’s with some on sale at $10 and others at $15. If you spent $315, how many were on sale?

51. Answer: 12 were on sale x + y = 25 10x + 15y = 315 Back to the Game Board Miscellaneous for 4

52. Question:Graph x > 1 y > 1 y ≤ 4 – 2x Check Your Answer Miscellaneous for 5

53. Answer: Back to the Game Board Miscellaneous for 5