The document discusses solving systems of linear equations. It provides examples of solving systems graphically and algebraically. Example 1 shows solving the system x + y = 3 and -2x + y = -6 by graphing the lines defined by each equation on the same xy-plane and finding their point of intersection, which is the solution to the system.

1. Section 1-6
Solving Systems of Equations

2. Essential Questions
• How do you solve systems of linear equations
graphically?
• How do you solve systems of linear equations
algebraically?

3. Vocabulary
1. System of Equations:
2. Consistent:
3. Inconsistent:
4. Independent:
5. Dependent:

4. Vocabulary
1. System of Equations:
2. Consistent:
3. Inconsistent:
4. Independent:
5. Dependent:
Two or more equations with
the same variables

5. Vocabulary
1. System of Equations:
2. Consistent:
3. Inconsistent:
4. Independent:
5. Dependent:
Two or more equations with
the same variables
A system with at least one solution

6. Vocabulary
1. System of Equations:
2. Consistent:
3. Inconsistent:
4. Independent:
5. Dependent:
Two or more equations with
the same variables
A system with at least one solution
A system with no solutions

7. Vocabulary
1. System of Equations:
2. Consistent:
3. Inconsistent:
4. Independent:
5. Dependent:
Two or more equations with
the same variables
A system with at least one solution
A system with no solutions
A system with exactly one solution

8. Vocabulary
1. System of Equations:
2. Consistent:
3. Inconsistent:
4. Independent:
5. Dependent:
Two or more equations with
the same variables
A system with at least one solution
A system with no solutions
A system with exactly one solution
A system with infinite solutions

9. Example 1
Solve the system of equations by graphing.
x + y = 3
−2x + y = −6
⎧
⎨
⎩

10. Example 1
Solve the system of equations by graphing.
x + y = 3
−2x + y = −6
⎧
⎨
⎩
x + y = 3

11. Example 1
Solve the system of equations by graphing.
x + y = 3
−2x + y = −6
⎧
⎨
⎩
x + y = 3
−x −x

12. Example 1
Solve the system of equations by graphing.
x + y = 3
−2x + y = −6
⎧
⎨
⎩
x + y = 3
−x −x
y = −x + 3

13. Example 1
Solve the system of equations by graphing.
x + y = 3
−2x + y = −6
⎧
⎨
⎩
x + y = 3
−x −x
y = −x + 3
m = −1
y − int = (0,3)

14. Example 1
Solve the system of equations by graphing.
x + y = 3
−2x + y = −6
⎧
⎨
⎩
x + y = 3
−x −x
y = −x + 3
m = −1
y − int = (0,3)
−2x + y = −6

15. Example 1
Solve the system of equations by graphing.
x + y = 3
−2x + y = −6
⎧
⎨
⎩
x + y = 3
−x −x
y = −x + 3
m = −1
y − int = (0,3)
−2x + y = −6
+2x +2x

16. Example 1
Solve the system of equations by graphing.
x + y = 3
−2x + y = −6
⎧
⎨
⎩
x + y = 3
−x −x
y = −x + 3
m = −1
y − int = (0,3)
−2x + y = −6
+2x +2x
y = 2x − 6

17. Example 1
Solve the system of equations by graphing.
x + y = 3
−2x + y = −6
⎧
⎨
⎩
x + y = 3
−x −x
y = −x + 3
m = −1
y − int = (0,3)
−2x + y = −6
+2x +2x
y = 2x − 6
m = 2
y − int = (0,−6)

18. Example 1
Solve the system of equations by graphing.
x + y = 3
−2x + y = −6
⎧
⎨
⎩
x + y = 3
−x −x
y = −x + 3
m = −1
y − int = (0,3)
−2x + y = −6
+2x +2x
y = 2x − 6
m = 2
y − int = (0,−6)
x
y

19. Example 1
Solve the system of equations by graphing.
x + y = 3
−2x + y = −6
⎧
⎨
⎩
x + y = 3
−x −x
y = −x + 3
m = −1
y − int = (0,3)
−2x + y = −6
+2x +2x
y = 2x − 6
m = 2
y − int = (0,−6)
x
y

20. Example 1
Solve the system of equations by graphing.
x + y = 3
−2x + y = −6
⎧
⎨
⎩
x + y = 3
−x −x
y = −x + 3
m = −1
y − int = (0,3)
−2x + y = −6
+2x +2x
y = 2x − 6
m = 2
y − int = (0,−6)
x
y

21. Example 1
Solve the system of equations by graphing.
x + y = 3
−2x + y = −6
⎧
⎨
⎩
x + y = 3
−x −x
y = −x + 3
m = −1
y − int = (0,3)
−2x + y = −6
+2x +2x
y = 2x − 6
m = 2
y − int = (0,−6)
x
y

22. Example 1
Solve the system of equations by graphing.
x + y = 3
−2x + y = −6
⎧
⎨
⎩
x + y = 3
−x −x
y = −x + 3
m = −1
y − int = (0,3)
−2x + y = −6
+2x +2x
y = 2x − 6
m = 2
y − int = (0,−6)
x
y

23. Example 1
Solve the system of equations by graphing.
x + y = 3
−2x + y = −6
⎧
⎨
⎩
x + y = 3
−x −x
y = −x + 3
m = −1
y − int = (0,3)
−2x + y = −6
+2x +2x
y = 2x − 6
m = 2
y − int = (0,−6)
x
y

24. Example 1
Solve the system of equations by graphing.
x + y = 3
−2x + y = −6
⎧
⎨
⎩
x + y = 3
−x −x
y = −x + 3
m = −1
y − int = (0,3)
−2x + y = −6
+2x +2x
y = 2x − 6
m = 2
y − int = (0,−6)
x
y

25. Example 1
Solve the system of equations by graphing.
x + y = 3
−2x + y = −6
⎧
⎨
⎩
x + y = 3
−x −x
y = −x + 3
m = −1
y − int = (0,3)
−2x + y = −6
+2x +2x
y = 2x − 6
m = 2
y − int = (0,−6)
x
y

26. Example 1
Solve the system of equations by graphing.
x + y = 3
−2x + y = −6
⎧
⎨
⎩
x + y = 3
−x −x
y = −x + 3
m = −1
y − int = (0,3)
−2x + y = −6
+2x +2x
y = 2x − 6
m = 2
y − int = (0,−6)
x
y

27. Example 1
Solve the system of equations by graphing.
x + y = 3
−2x + y = −6
⎧
⎨
⎩
x + y = 3
−x −x
y = −x + 3
m = −1
y − int = (0,3)
−2x + y = −6
+2x +2x
y = 2x − 6
m = 2
y − int = (0,−6)
x
y

28. Example 1
Solve the system of equations by graphing.
x + y = 3
−2x + y = −6
⎧
⎨
⎩
x + y = 3
−x −x
y = −x + 3
m = −1
y − int = (0,3)
−2x + y = −6
+2x +2x
y = 2x − 6
m = 2
y − int = (0,−6)
x
y

29. Example 1
Solve the system of equations by graphing.
x + y = 3
−2x + y = −6
⎧
⎨
⎩
x + y = 3
−x −x
y = −x + 3
m = −1
y − int = (0,3)
−2x + y = −6
+2x +2x
y = 2x − 6
m = 2
y − int = (0,−6)
x
y

30. Example 1
Solve the system of equations by graphing.
x + y = 3
−2x + y = −6
⎧
⎨
⎩
x + y = 3
−x −x
y = −x + 3
m = −1
y − int = (0,3)
−2x + y = −6
+2x +2x
y = 2x − 6
m = 2
y − int = (0,−6)
x
y

31. Example 1
Solve the system of equations by graphing.
x + y = 3
−2x + y = −6
⎧
⎨
⎩
x + y = 3
−x −x
y = −x + 3
m = −1
y − int = (0,3)
−2x + y = −6
+2x +2x
y = 2x − 6
m = 2
y − int = (0,−6)
x
y

32. Example 1
Solve the system of equations by graphing.
x + y = 3
−2x + y = −6
⎧
⎨
⎩
x + y = 3
−x −x
y = −x + 3
m = −1
y − int = (0,3)
−2x + y = −6
+2x +2x
y = 2x − 6
m = 2
y − int = (0,−6)
x
y

33. Example 1
Solve the system of equations by graphing.
x + y = 3
−2x + y = −6
⎧
⎨
⎩
x + y = 3
−x −x
y = −x + 3
m = −1
y − int = (0,3)
−2x + y = −6
+2x +2x
y = 2x − 6
m = 2
y − int = (0,−6)
x
y

34. Example 1
Solve the system of equations by graphing.
x + y = 3
−2x + y = −6
⎧
⎨
⎩
x + y = 3
−x −x
y = −x + 3
m = −1
y − int = (0,3)
−2x + y = −6
+2x +2x
y = 2x − 6
m = 2
y − int = (0,−6)
x
y

35. Example 1
Solve the system of equations by graphing.
x + y = 3
−2x + y = −6
⎧
⎨
⎩
x + y = 3
−x −x
y = −x + 3
m = −1
y − int = (0,3)
−2x + y = −6
+2x +2x
y = 2x − 6
m = 2
y − int = (0,−6)
x
y

36. Example 1
Solve the system of equations by graphing.
x + y = 3
−2x + y = −6
⎧
⎨
⎩
x + y = 3
−x −x
y = −x + 3
m = −1
y − int = (0,3)
−2x + y = −6
+2x +2x
y = 2x − 6
m = 2
y − int = (0,−6)
x
y

37. Example 1
Solve the system of equations by graphing.
x + y = 3
−2x + y = −6
⎧
⎨
⎩
x + y = 3
−x −x
y = −x + 3
m = −1
y − int = (0,3)
−2x + y = −6
+2x +2x
y = 2x − 6
m = 2
y − int = (0,−6)
x
y

38. Example 1
Solve the system of equations by graphing.
x + y = 3
−2x + y = −6
⎧
⎨
⎩
x + y = 3
−x −x
y = −x + 3
m = −1
y − int = (0,3)
−2x + y = −6
+2x +2x
y = 2x − 6
m = 2
y − int = (0,−6)
x
y

39. Example 1
Solve the system of equations by graphing.
x + y = 3
−2x + y = −6
⎧
⎨
⎩
x + y = 3
−x −x
y = −x + 3
m = −1
y − int = (0,3)
−2x + y = −6
+2x +2x
y = 2x − 6
m = 2
y − int = (0,−6)
x
y

40. Example 1
Solve the system of equations by graphing.
x + y = 3
−2x + y = −6
⎧
⎨
⎩
x + y = 3
−x −x
y = −x + 3
m = −1
y − int = (0,3)
−2x + y = −6
+2x +2x
y = 2x − 6
m = 2
y − int = (0,−6)
x
y

41. Example 1
Solve the system of equations by graphing.
x + y = 3
−2x + y = −6
⎧
⎨
⎩
x + y = 3
−x −x
y = −x + 3
m = −1
y − int = (0,3)
−2x + y = −6
+2x +2x
y = 2x − 6
m = 2
y − int = (0,−6)
x
y

42. Example 1
Solve the system of equations by graphing.
x + y = 3
−2x + y = −6
⎧
⎨
⎩
x + y = 3
−x −x
y = −x + 3
m = −1
y − int = (0,3)
−2x + y = −6
+2x +2x
y = 2x − 6
m = 2
y − int = (0,−6)
x
y

43. Example 1
Solve the system of equations by graphing.
x + y = 3
−2x + y = −6
⎧
⎨
⎩
x + y = 3
−x −x
y = −x + 3
m = −1
y − int = (0,3)
−2x + y = −6
+2x +2x
y = 2x − 6
m = 2
y − int = (0,−6)
x
y

44. Example 1
Solve the system of equations by graphing.
x + y = 3
−2x + y = −6
⎧
⎨
⎩
x + y = 3
−x −x
y = −x + 3
m = −1
y − int = (0,3)
−2x + y = −6
+2x +2x
y = 2x − 6
m = 2
y − int = (0,−6)
x
y

45. Example 1
Solve the system of equations by graphing.
x + y = 3
−2x + y = −6
⎧
⎨
⎩
x + y = 3
−x −x
y = −x + 3
m = −1
y − int = (0,3)
−2x + y = −6
+2x +2x
y = 2x − 6
m = 2
y − int = (0,−6)
x
y

46. Example 1
Solve the system of equations by graphing.
x + y = 3
−2x + y = −6
⎧
⎨
⎩
x + y = 3
−x −x
y = −x + 3
m = −1
y − int = (0,3)
−2x + y = −6
+2x +2x
y = 2x − 6
m = 2
y − int = (0,−6)
x
y
(3,0)

47. Example 1
Solve the system of equations by graphing.
x + y = 3
−2x + y = −6
⎧
⎨
⎩
x + y = 3
−x −x
y = −x + 3
m = −1
y − int = (0,3)
−2x + y = −6
+2x +2x
y = 2x − 6
m = 2
y − int = (0,−6)
x
y
(3,0)
Check:

48. Example 1
Solve the system of equations by graphing.
x + y = 3
−2x + y = −6
⎧
⎨
⎩
x + y = 3
−x −x
y = −x + 3
m = −1
y − int = (0,3)
−2x + y = −6
+2x +2x
y = 2x − 6
m = 2
y − int = (0,−6)
x
y
(3,0)
Check: 3 + 0 = 3

49. Example 1
Solve the system of equations by graphing.
x + y = 3
−2x + y = −6
⎧
⎨
⎩
x + y = 3
−x −x
y = −x + 3
m = −1
y − int = (0,3)
−2x + y = −6
+2x +2x
y = 2x − 6
m = 2
y − int = (0,−6)
x
y
(3,0)
Check: 3 + 0 = 3 −2(3)+ 0 = −6

50. Example 2
Solve the system of equations by substitution.
x − 2y = 0
y = −x + 6
⎧
⎨
⎩

51. Example 2
Solve the system of equations by substitution.
x − 2y = 0
y = −x + 6
⎧
⎨
⎩
x − 2(−x + 6)= 0

52. Example 2
Solve the system of equations by substitution.
x − 2y = 0
y = −x + 6
⎧
⎨
⎩
x − 2(−x + 6)= 0
x + 2x −12 = 0

53. Example 2
Solve the system of equations by substitution.
x − 2y = 0
y = −x + 6
⎧
⎨
⎩
x − 2(−x + 6)= 0
x + 2x −12 = 0
3x −12 = 0

54. Example 2
Solve the system of equations by substitution.
x − 2y = 0
y = −x + 6
⎧
⎨
⎩
x − 2(−x + 6)= 0
x + 2x −12 = 0
3x −12 = 0
+12+12

55. Example 2
Solve the system of equations by substitution.
x − 2y = 0
y = −x + 6
⎧
⎨
⎩
x − 2(−x + 6)= 0
x + 2x −12 = 0
3x −12 = 0
+12+12
3x = 12

56. Example 2
Solve the system of equations by substitution.
x − 2y = 0
y = −x + 6
⎧
⎨
⎩
x − 2(−x + 6)= 0
x + 2x −12 = 0
3x −12 = 0
+12+12
3x = 12
3 3

57. Example 2
Solve the system of equations by substitution.
x − 2y = 0
y = −x + 6
⎧
⎨
⎩
x − 2(−x + 6)= 0
x + 2x −12 = 0
3x −12 = 0
+12+12
3x = 12
3 3
x = 4

58. Example 2
Solve the system of equations by substitution.
x − 2y = 0
y = −x + 6
⎧
⎨
⎩
x − 2(−x + 6)= 0
x + 2x −12 = 0
3x −12 = 0
+12+12
3x = 12
3 3
x = 4
y = −4 + 6

59. Example 2
Solve the system of equations by substitution.
x − 2y = 0
y = −x + 6
⎧
⎨
⎩
x − 2(−x + 6)= 0
x + 2x −12 = 0
3x −12 = 0
+12+12
3x = 12
3 3
x = 4
y = −4 + 6
y = 2

60. Example 2
Solve the system of equations by substitution.
x − 2y = 0
y = −x + 6
⎧
⎨
⎩
x − 2(−x + 6)= 0
x + 2x −12 = 0
3x −12 = 0
+12+12
3x = 12
3 3
x = 4
y = −4 + 6
y = 2 (4,2)

61. Example 2
Solve the system of equations by substitution.
x − 2y = 0
y = −x + 6
⎧
⎨
⎩
x − 2(−x + 6)= 0
Check:
x + 2x −12 = 0
3x −12 = 0
+12+12
3x = 12
3 3
x = 4
y = −4 + 6
y = 2 (4,2)

62. Example 2
Solve the system of equations by substitution.
x − 2y = 0
y = −x + 6
⎧
⎨
⎩
x − 2(−x + 6)= 0
Check:
4 − 2(2) = 0x + 2x −12 = 0
3x −12 = 0
+12+12
3x = 12
3 3
x = 4
y = −4 + 6
y = 2 (4,2)

63. Example 2
Solve the system of equations by substitution.
x − 2y = 0
y = −x + 6
⎧
⎨
⎩
x − 2(−x + 6)= 0
Check:
4 − 2(2) = 0 2 = −4 + 6x + 2x −12 = 0
3x −12 = 0
+12+12
3x = 12
3 3
x = 4
y = −4 + 6
y = 2 (4,2)

64. Example 3
Solve the system of equations by elimination.
x + 2y = 10
x + y = 6
⎧
⎨
⎩

65. Example 3
Solve the system of equations by elimination.
x + 2y = 10
x + y = 6
⎧
⎨
⎩
x + 2y = 10
(−1)(x + y = 6)

66. Example 3
Solve the system of equations by elimination.
x + 2y = 10
x + y = 6
⎧
⎨
⎩
x + 2y = 10
(−1)(x + y = 6)
x + 2y = 10
−x − y = −6

67. Example 3
Solve the system of equations by elimination.
x + 2y = 10
x + y = 6
⎧
⎨
⎩
x + 2y = 10
(−1)(x + y = 6)
x + 2y = 10
−x − y = −6
y = 4

68. Example 3
Solve the system of equations by elimination.
x + 2y = 10
x + y = 6
⎧
⎨
⎩
x + 4 = 6
x + 2y = 10
(−1)(x + y = 6)
x + 2y = 10
−x − y = −6
y = 4

69. Example 3
Solve the system of equations by elimination.
x + 2y = 10
x + y = 6
⎧
⎨
⎩
x + 4 = 6
x + 2y = 10
(−1)(x + y = 6)
x + 2y = 10
−x − y = −6
y = 4
−4 −4

70. Example 3
Solve the system of equations by elimination.
x + 2y = 10
x + y = 6
⎧
⎨
⎩
x + 4 = 6
x = 2
x + 2y = 10
(−1)(x + y = 6)
x + 2y = 10
−x − y = −6
y = 4
−4 −4

71. Example 3
Solve the system of equations by elimination.
x + 2y = 10
x + y = 6
⎧
⎨
⎩
x + 4 = 6
x = 2
(2,4)
x + 2y = 10
(−1)(x + y = 6)
x + 2y = 10
−x − y = −6
y = 4
−4 −4

72. Example 3
Solve the system of equations by elimination.
x + 2y = 10
x + y = 6
⎧
⎨
⎩
Check:
x + 4 = 6
x = 2
(2,4)
x + 2y = 10
(−1)(x + y = 6)
x + 2y = 10
−x − y = −6
y = 4
−4 −4

73. Example 3
Solve the system of equations by elimination.
x + 2y = 10
x + y = 6
⎧
⎨
⎩
Check:
2+ 2(4) = 10
x + 4 = 6
x = 2
(2,4)
x + 2y = 10
(−1)(x + y = 6)
x + 2y = 10
−x − y = −6
y = 4
−4 −4

74. Example 3
Solve the system of equations by elimination.
x + 2y = 10
x + y = 6
⎧
⎨
⎩
Check:
2+ 2(4) = 10 2+ 4 = 6
x + 4 = 6
x = 2
(2,4)
x + 2y = 10
(−1)(x + y = 6)
x + 2y = 10
−x − y = −6
y = 4
−4 −4

75. Example 4
Shecky’s Furniture Works builds two types of
wooden outdoor chairs. A rocking chair sells for
$265, and an Adirondack chair with a footstool
sells for $320. The books show that last month, the
business earned $13,930 for the 48 outdoor chairs
sold. How many rocking chairs were sold?

76. Example 4
Shecky’s Furniture Works builds two types of
wooden outdoor chairs. A rocking chair sells for
$265, and an Adirondack chair with a footstool
sells for $320. The books show that last month, the
business earned $13,930 for the 48 outdoor chairs
sold. How many rocking chairs were sold?
x = rocking chair

77. Example 4
Shecky’s Furniture Works builds two types of
wooden outdoor chairs. A rocking chair sells for
$265, and an Adirondack chair with a footstool
sells for $320. The books show that last month, the
business earned $13,930 for the 48 outdoor chairs
sold. How many rocking chairs were sold?
x = rocking chair
y = Adirondack chair

78. Example 4
Shecky’s Furniture Works builds two types of
wooden outdoor chairs. A rocking chair sells for
$265, and an Adirondack chair with a footstool
sells for $320. The books show that last month, the
business earned $13,930 for the 48 outdoor chairs
sold. How many rocking chairs were sold?
x = rocking chair
y = Adirondack chair
x + y = 48
265x + 320y = 13,930
⎧
⎨
⎩

79. Example 4
x + y = 48
265x + 320y = 13,930
⎧
⎨
⎩

80. Example 4
x + y = 48
265x + 320y = 13,930
⎧
⎨
⎩
x + y = 48

81. Example 4
x + y = 48
265x + 320y = 13,930
⎧
⎨
⎩
x + y = 48
y = −x + 48

82. Example 4
x + y = 48
265x + 320y = 13,930
⎧
⎨
⎩
x + y = 48
y = −x + 48
265x + 320(−x + 48) = 13,930

83. Example 4
x + y = 48
265x + 320y = 13,930
⎧
⎨
⎩
x + y = 48
y = −x + 48
265x + 320(−x + 48) = 13,930
265x − 320x +15,360 = 13,930

84. Example 4
x + y = 48
265x + 320y = 13,930
⎧
⎨
⎩
x + y = 48
y = −x + 48
265x + 320(−x + 48) = 13,930
265x − 320x +15,360 = 13,930
−55x +15,360 = 13,930

85. Example 4
x + y = 48
265x + 320y = 13,930
⎧
⎨
⎩
x + y = 48
y = −x + 48
265x + 320(−x + 48) = 13,930
265x − 320x +15,360 = 13,930
−55x +15,360 = 13,930
−15,360 −15,360

86. Example 4
x + y = 48
265x + 320y = 13,930
⎧
⎨
⎩
x + y = 48
y = −x + 48
265x + 320(−x + 48) = 13,930
265x − 320x +15,360 = 13,930
−55x +15,360 = 13,930
−15,360 −15,360
−55x = −1430

87. Example 4
x + y = 48
265x + 320y = 13,930
⎧
⎨
⎩
x + y = 48
y = −x + 48
265x + 320(−x + 48) = 13,930
265x − 320x +15,360 = 13,930
−55x +15,360 = 13,930
−15,360 −15,360
−55x = −1430
−55 −55

88. Example 4
x + y = 48
265x + 320y = 13,930
⎧
⎨
⎩
x + y = 48
y = −x + 48
265x + 320(−x + 48) = 13,930
265x − 320x +15,360 = 13,930
−55x +15,360 = 13,930
−15,360 −15,360
−55x = −1430
−55 −55
x = 26

89. Example 4
26 + y = 48x + y = 48
265x + 320y = 13,930
⎧
⎨
⎩
x + y = 48
y = −x + 48
265x + 320(−x + 48) = 13,930
265x − 320x +15,360 = 13,930
−55x +15,360 = 13,930
−15,360 −15,360
−55x = −1430
−55 −55
x = 26

90. Example 4
26 + y = 48
−26 −26
x + y = 48
265x + 320y = 13,930
⎧
⎨
⎩
x + y = 48
y = −x + 48
265x + 320(−x + 48) = 13,930
265x − 320x +15,360 = 13,930
−55x +15,360 = 13,930
−15,360 −15,360
−55x = −1430
−55 −55
x = 26

91. Example 4
26 + y = 48
y = 22
−26 −26
x + y = 48
265x + 320y = 13,930
⎧
⎨
⎩
x + y = 48
y = −x + 48
265x + 320(−x + 48) = 13,930
265x − 320x +15,360 = 13,930
−55x +15,360 = 13,930
−15,360 −15,360
−55x = −1430
−55 −55
x = 26

92. Example 4
26 + y = 48
y = 22
(26,22)
−26 −26
x + y = 48
265x + 320y = 13,930
⎧
⎨
⎩
x + y = 48
y = −x + 48
265x + 320(−x + 48) = 13,930
265x − 320x +15,360 = 13,930
−55x +15,360 = 13,930
−15,360 −15,360
−55x = −1430
−55 −55
x = 26

93. Example 4
Check:
26 + y = 48
y = 22
(26,22)
−26 −26
x + y = 48
265x + 320y = 13,930
⎧
⎨
⎩
x + y = 48
y = −x + 48
265x + 320(−x + 48) = 13,930
265x − 320x +15,360 = 13,930
−55x +15,360 = 13,930
−15,360 −15,360
−55x = −1430
−55 −55
x = 26

94. Example 4
Check:
26 + 22 = 48
26 + y = 48
y = 22
(26,22)
−26 −26
x + y = 48
265x + 320y = 13,930
⎧
⎨
⎩
x + y = 48
y = −x + 48
265x + 320(−x + 48) = 13,930
265x − 320x +15,360 = 13,930
−55x +15,360 = 13,930
−15,360 −15,360
−55x = −1430
−55 −55
x = 26

95. Example 4
Check:
26 + 22 = 48
265(26)+ 320(22)= 13,930
26 + y = 48
y = 22
(26,22)
−26 −26
x + y = 48
265x + 320y = 13,930
⎧
⎨
⎩
x + y = 48
y = −x + 48
265x + 320(−x + 48) = 13,930
265x − 320x +15,360 = 13,930
−55x +15,360 = 13,930
−15,360 −15,360
−55x = −1430
−55 −55
x = 26

96. Example 4
Check:
26 + 22 = 48
265(26)+ 320(22)= 13,930
26 + y = 48
y = 22
(26,22)
−26 −26
x + y = 48
265x + 320y = 13,930
⎧
⎨
⎩
x + y = 48
y = −x + 48
265x + 320(−x + 48) = 13,930
265x − 320x +15,360 = 13,930
−55x +15,360 = 13,930
−15,360 −15,360
−55x = −1430
−55 −55
x = 26
6890 + 7040 = 13,930

97. Example 4
Check:
26 + 22 = 48
265(26)+ 320(22)= 13,930
26 + y = 48
y = 22
(26,22)
−26 −26
x + y = 48
265x + 320y = 13,930
⎧
⎨
⎩
x + y = 48
y = −x + 48
265x + 320(−x + 48) = 13,930
265x − 320x +15,360 = 13,930
−55x +15,360 = 13,930
−15,360 −15,360
−55x = −1430
−55 −55
x = 26
6890 + 7040 = 13,930
26 rocking chairs
were sold

98. Example 5
Solve the system of equations.
a.
2x + 4y = 12
−5x −10y = −30
⎧
⎨
⎩

99. Example 5
Solve the system of equations.
a.
2x + 4y = 12
−5x −10y = −30
⎧
⎨
⎩
(5)(2x + 4y = 12)
(2)(−5x −10y = −30)

100. Example 5
Solve the system of equations.
a.
2x + 4y = 12
−5x −10y = −30
⎧
⎨
⎩
(5)(2x + 4y = 12)
(2)(−5x −10y = −30)
10x + 20y = 60
−10x − 20y = −60

101. Example 5
Solve the system of equations.
a.
2x + 4y = 12
−5x −10y = −30
⎧
⎨
⎩
(5)(2x + 4y = 12)
(2)(−5x −10y = −30)
10x + 20y = 60
−10x − 20y = −60
0 = 0

102. Example 5
Solve the system of equations.
a.
2x + 4y = 12
−5x −10y = −30
⎧
⎨
⎩
(5)(2x + 4y = 12)
(2)(−5x −10y = −30)
10x + 20y = 60
−10x − 20y = −60
0 = 0
Infinite solutions
on the line

103. Example 5
Solve the system of equations.
b.
15x − 6y = 0
5x − 2y = 10
⎧
⎨
⎩

104. Example 5
Solve the system of equations.
b.
15x − 6y = 0
5x − 2y = 10
⎧
⎨
⎩
15x − 6y = 0
(−3)(5x − 2y = 10)

105. Example 5
Solve the system of equations.
b.
15x − 6y = 0
5x − 2y = 10
⎧
⎨
⎩
15x − 6y = 0
(−3)(5x − 2y = 10)
15x − 6y = 0
−15x + 6y = −30

106. Example 5
Solve the system of equations.
b.
15x − 6y = 0
5x − 2y = 10
⎧
⎨
⎩
15x − 6y = 0
(−3)(5x − 2y = 10)
15x − 6y = 0
−15x + 6y = −30
0 = −30

107. Example 5
Solve the system of equations.
b.
15x − 6y = 0
5x − 2y = 10
⎧
⎨
⎩
15x − 6y = 0
(−3)(5x − 2y = 10)
15x − 6y = 0
−15x + 6y = −30
0 = −30
No solutions