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# Int Math 2 Section 8-4 1011

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Solve Systems by Adding, Subtracting, and Multiplying (Linear Combinations)

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### Int Math 2 Section 8-4 1011

1. 1. Section 8-4 Solve Systems by Adding, Subtracting, and Multiplying (Linear Combinations)Sun, Apr 10
2. 2. Essential Questions How do you solve systems of equations by adding and subtracting? How do you solve systems of equations by adding and multiplying? Where you’ll see this: Landscaping, construction, sportsSun, Apr 10
3. 3. Why another method?Sun, Apr 10
4. 4. Why another method? Graphing: Problems with accuracySun, Apr 10
5. 5. Why another method? Graphing: Problems with accuracy Substitution: Need an isolated variableSun, Apr 10
6. 6. Why another method? Graphing: Problems with accuracy Substitution: Need an isolated variable Combinations: Could speed up processSun, Apr 10
7. 7. Why another method? Graphing: Problems with accuracy Substitution: Need an isolated variable Combinations: Could speed up process Look at the system to determine best methodSun, Apr 10
8. 8. Solve by CombinationsSun, Apr 10
9. 9. Solve by Combinations 1. Choose a variable to eliminate (your choice).Sun, Apr 10
10. 10. Solve by Combinations 1. Choose a variable to eliminate (your choice). 2. Make the coefﬁcients of that variable opposite. You might need to multiply to do this. Then combine equations.Sun, Apr 10
11. 11. Solve by Combinations 1. Choose a variable to eliminate (your choice). 2. Make the coefﬁcients of that variable opposite. You might need to multiply to do this. Then combine equations. 3. Solve for the remaining variable.Sun, Apr 10
12. 12. Solve by Combinations 1. Choose a variable to eliminate (your choice). 2. Make the coefﬁcients of that variable opposite. You might need to multiply to do this. Then combine equations. 3. Solve for the remaining variable. 4. Plug back into an original equation to ﬁnd the other variable.Sun, Apr 10
13. 13. Solve by Combinations 1. Choose a variable to eliminate (your choice). 2. Make the coefﬁcients of that variable opposite. You might need to multiply to do this. Then combine equations. 3. Solve for the remaining variable. 4. Plug back into an original equation to ﬁnd the other variable. 5. Check and rewrite the answer.Sun, Apr 10
14. 14. Example 1 Solve by combining the equations ⎧−2x + 3 y = 2 ⎪ a. ⎨ ⎪ 2x + 7 y = 18 ⎩Sun, Apr 10
15. 15. Example 1 Solve by combining the equations ⎧−2x + 3 y = 2 ⎪ a. ⎨ ⎪ 2x + 7 y = 18 ⎩ −2x + 3 y = 2Sun, Apr 10
16. 16. Example 1 Solve by combining the equations ⎧−2x + 3 y = 2 ⎪ a. ⎨ ⎪ 2x + 7 y = 18 ⎩ −2x + 3 y = 2 2x + 7 y = 18Sun, Apr 10
17. 17. Example 1 Solve by combining the equations ⎧−2x + 3 y = 2 ⎪ a. ⎨ ⎪ 2x + 7 y = 18 ⎩ −2x + 3 y = 2 2x + 7 y = 18Sun, Apr 10
18. 18. Example 1 Solve by combining the equations ⎧−2x + 3 y = 2 ⎪ a. ⎨ ⎪ 2x + 7 y = 18 ⎩ −2x + 3 y = 2 2x + 7 y = 18 10 y = 20Sun, Apr 10
19. 19. Example 1 Solve by combining the equations ⎧−2x + 3 y = 2 ⎪ a. ⎨ ⎪ 2x + 7 y = 18 ⎩ −2x + 3 y = 2 2x + 7 y = 18 10 y = 20 10 10Sun, Apr 10
20. 20. Example 1 Solve by combining the equations ⎧−2x + 3 y = 2 ⎪ a. ⎨ ⎪ 2x + 7 y = 18 ⎩ −2x + 3 y = 2 2x + 7 y = 18 10 y = 20 10 10 y=2Sun, Apr 10
21. 21. Example 1 Solve by combining the equations ⎧−2x + 3 y = 2 ⎪ a. ⎨ ⎪ 2x + 7 y = 18 ⎩ −2x + 3 y = 2 −2x + 3(2) = 2 2x + 7 y = 18 10 y = 20 10 10 y=2Sun, Apr 10
22. 22. Example 1 Solve by combining the equations ⎧−2x + 3 y = 2 ⎪ a. ⎨ ⎪ 2x + 7 y = 18 ⎩ −2x + 3 y = 2 −2x + 3(2) = 2 2x + 7 y = 18 −2x + 6 = 2 10 y = 20 10 10 y=2Sun, Apr 10
23. 23. Example 1 Solve by combining the equations ⎧−2x + 3 y = 2 ⎪ a. ⎨ ⎪ 2x + 7 y = 18 ⎩ −2x + 3 y = 2 −2x + 3(2) = 2 2x + 7 y = 18 −2x + 6 = 2 10 y = 20 −6 −6 10 10 y=2Sun, Apr 10
24. 24. Example 1 Solve by combining the equations ⎧−2x + 3 y = 2 ⎪ a. ⎨ ⎪ 2x + 7 y = 18 ⎩ −2x + 3 y = 2 −2x + 3(2) = 2 2x + 7 y = 18 −2x + 6 = 2 10 y = 20 −6 −6 10 10 −2x = −4 y=2Sun, Apr 10
25. 25. Example 1 Solve by combining the equations ⎧−2x + 3 y = 2 ⎪ a. ⎨ ⎪ 2x + 7 y = 18 ⎩ −2x + 3 y = 2 −2x + 3(2) = 2 2x + 7 y = 18 −2x + 6 = 2 10 y = 20 −6 −6 10 10 −2x = −4 y=2 −2 −2Sun, Apr 10
26. 26. Example 1 Solve by combining the equations ⎧−2x + 3 y = 2 ⎪ a. ⎨ ⎪ 2x + 7 y = 18 ⎩ −2x + 3 y = 2 −2x + 3(2) = 2 2x + 7 y = 18 −2x + 6 = 2 10 y = 20 −6 −6 10 10 −2x = −4 y=2 −2 −2 x=2Sun, Apr 10
27. 27. Example 1 Solve by combining the equations ⎧−2x + 3 y = 2 ⎪ a. ⎨ ⎪ 2x + 7 y = 18 ⎩ Check: −2x + 3 y = 2 −2x + 3(2) = 2 2x + 7 y = 18 −2x + 6 = 2 10 y = 20 −6 −6 10 10 −2x = −4 y=2 −2 −2 x=2Sun, Apr 10
28. 28. Example 1 Solve by combining the equations ⎧−2x + 3 y = 2 ⎪ a. ⎨ ⎪ 2x + 7 y = 18 ⎩ Check: −2x + 3 y = 2 −2(2) + 3(2) = 2 −2x + 3(2) = 2 2x + 7 y = 18 −2x + 6 = 2 10 y = 20 −6 −6 10 10 −2x = −4 y=2 −2 −2 x=2Sun, Apr 10
29. 29. Example 1 Solve by combining the equations ⎧−2x + 3 y = 2 ⎪ a. ⎨ ⎪ 2x + 7 y = 18 ⎩ Check: −2x + 3 y = 2 −2(2) + 3(2) = 2 −2x + 3(2) = 2 2x + 7 y = 18 −4 + 6 = 2 −2x + 6 = 2 10 y = 20 −6 −6 10 10 −2x = −4 y=2 −2 −2 x=2Sun, Apr 10
30. 30. Example 1 Solve by combining the equations ⎧−2x + 3 y = 2 ⎪ a. ⎨ ⎪ 2x + 7 y = 18 ⎩ Check: −2x + 3 y = 2 −2(2) + 3(2) = 2 −2x + 3(2) = 2 2x + 7 y = 18 −4 + 6 = 2 −2x + 6 = 2 10 y = 20 −6 −6 2(2) + 7(2) = 18 10 10 −2x = −4 y=2 −2 −2 x=2Sun, Apr 10
31. 31. Example 1 Solve by combining the equations ⎧−2x + 3 y = 2 ⎪ a. ⎨ ⎪ 2x + 7 y = 18 ⎩ Check: −2x + 3 y = 2 −2(2) + 3(2) = 2 −2x + 3(2) = 2 2x + 7 y = 18 −4 + 6 = 2 −2x + 6 = 2 10 y = 20 −6 −6 2(2) + 7(2) = 18 10 10 −2x = −4 4 + 14 = 18 y=2 −2 −2 x=2Sun, Apr 10
32. 32. Example 1 Solve by combining the equations ⎧−2x + 3 y = 2 ⎪ a. ⎨ ⎪ 2x + 7 y = 18 ⎩ Check: −2x + 3 y = 2 −2(2) + 3(2) = 2 −2x + 3(2) = 2 2x + 7 y = 18 −4 + 6 = 2 −2x + 6 = 2 10 y = 20 −6 −6 2(2) + 7(2) = 18 10 10 −2x = −4 4 + 14 = 18 y=2 −2 −2 x=2 (2, 2)Sun, Apr 10
33. 33. Example 1 Solve by combining the equations ⎧10x + 4 y = 14 ⎪ b. ⎨ ⎪x + 4 y = 5 ⎩Sun, Apr 10
34. 34. Example 1 Solve by combining the equations ⎧10x + 4 y = 14 ⎪ b. ⎨ ⎪ x + 4 y = 5)(−1) ⎩(Sun, Apr 10
35. 35. Example 1 Solve by combining the equations ⎧10x + 4 y = 14 ⎪ b. ⎨ ⎪ x + 4 y = 5)(−1) ⎩( 10x + 4 y = 14Sun, Apr 10
36. 36. Example 1 Solve by combining the equations ⎧10x + 4 y = 14 ⎪ b. ⎨ ⎪ x + 4 y = 5)(−1) ⎩( 10x + 4 y = 14 − x − 4 y = −5Sun, Apr 10
37. 37. Example 1 Solve by combining the equations ⎧10x + 4 y = 14 ⎪ b. ⎨ ⎪ x + 4 y = 5)(−1) ⎩( 10x + 4 y = 14 − x − 4 y = −5Sun, Apr 10
38. 38. Example 1 Solve by combining the equations ⎧10x + 4 y = 14 ⎪ b. ⎨ ⎪ x + 4 y = 5)(−1) ⎩( 10x + 4 y = 14 − x − 4 y = −5 9x = 9Sun, Apr 10
39. 39. Example 1 Solve by combining the equations ⎧10x + 4 y = 14 ⎪ b. ⎨ ⎪ x + 4 y = 5)(−1) ⎩( 10x + 4 y = 14 − x − 4 y = −5 9x = 9 9 9Sun, Apr 10
40. 40. Example 1 Solve by combining the equations ⎧10x + 4 y = 14 ⎪ b. ⎨ ⎪ x + 4 y = 5)(−1) ⎩( 10x + 4 y = 14 − x − 4 y = −5 9x = 9 9 9 x=1Sun, Apr 10
41. 41. Example 1 Solve by combining the equations ⎧10x + 4 y = 14 ⎪ b. ⎨ ⎪ x + 4 y = 5)(−1) ⎩( 10x + 4 y = 14 − x − 4 y = −5 1+ 4 y = 5 9x = 9 9 9 x=1Sun, Apr 10
42. 42. Example 1 Solve by combining the equations ⎧10x + 4 y = 14 ⎪ b. ⎨ ⎪ x + 4 y = 5)(−1) ⎩( 10x + 4 y = 14 − x − 4 y = −5 1+ 4 y = 5 9x = 9 −1 −1 9 9 x=1Sun, Apr 10
43. 43. Example 1 Solve by combining the equations ⎧10x + 4 y = 14 ⎪ b. ⎨ ⎪ x + 4 y = 5)(−1) ⎩( 10x + 4 y = 14 − x − 4 y = −5 1+ 4 y = 5 9x = 9 −1 −1 9 9 4y = 4 x=1Sun, Apr 10
44. 44. Example 1 Solve by combining the equations ⎧10x + 4 y = 14 ⎪ b. ⎨ ⎪ x + 4 y = 5)(−1) ⎩( 10x + 4 y = 14 − x − 4 y = −5 1+ 4 y = 5 9x = 9 −1 −1 9 9 4y = 4 4 4 x=1Sun, Apr 10
45. 45. Example 1 Solve by combining the equations ⎧10x + 4 y = 14 ⎪ b. ⎨ ⎪ x + 4 y = 5)(−1) ⎩( 10x + 4 y = 14 − x − 4 y = −5 1+ 4 y = 5 9x = 9 −1 −1 9 9 4y = 4 4 4 x=1 y =1Sun, Apr 10
46. 46. Example 1 Solve by combining the equations ⎧10x + 4 y = 14 ⎪ b. ⎨ ⎪ x + 4 y = 5)(−1) ⎩( Check: 10x + 4 y = 14 − x − 4 y = −5 1+ 4 y = 5 9x = 9 −1 −1 9 9 4y = 4 4 4 x=1 y =1Sun, Apr 10
47. 47. Example 1 Solve by combining the equations ⎧10x + 4 y = 14 ⎪ b. ⎨ ⎪ x + 4 y = 5)(−1) ⎩( Check: 10x + 4 y = 14 − x − 4 y = −5 1+ 4 y = 5 10(1) + 4(1) = 14 9x = 9 −1 −1 9 9 4y = 4 4 4 x=1 y =1Sun, Apr 10
48. 48. Example 1 Solve by combining the equations ⎧10x + 4 y = 14 ⎪ b. ⎨ ⎪ x + 4 y = 5)(−1) ⎩( Check: 10x + 4 y = 14 − x − 4 y = −5 1+ 4 y = 5 10(1) + 4(1) = 14 9x = 9 −1 −1 10 + 4 = 14 9 9 4y = 4 4 4 x=1 y =1Sun, Apr 10
49. 49. Example 1 Solve by combining the equations ⎧10x + 4 y = 14 ⎪ b. ⎨ ⎪ x + 4 y = 5)(−1) ⎩( Check: 10x + 4 y = 14 − x − 4 y = −5 1+ 4 y = 5 10(1) + 4(1) = 14 9x = 9 −1 −1 10 + 4 = 14 9 9 4y = 4 4 4 1 + 4(1) = 5 x=1 y =1Sun, Apr 10
50. 50. Example 1 Solve by combining the equations ⎧10x + 4 y = 14 ⎪ b. ⎨ ⎪ x + 4 y = 5)(−1) ⎩( Check: 10x + 4 y = 14 − x − 4 y = −5 1+ 4 y = 5 10(1) + 4(1) = 14 9x = 9 −1 −1 10 + 4 = 14 9 9 4y = 4 4 4 1 + 4(1) = 5 x=1 1+ 4 = 5 y =1Sun, Apr 10
51. 51. Example 1 Solve by combining the equations ⎧10x + 4 y = 14 ⎪ b. ⎨ ⎪ x + 4 y = 5)(−1) ⎩( Check: 10x + 4 y = 14 − x − 4 y = −5 1+ 4 y = 5 10(1) + 4(1) = 14 9x = 9 −1 −1 10 + 4 = 14 9 9 4y = 4 4 4 1 + 4(1) = 5 x=1 1+ 4 = 5 y =1 (1,1)Sun, Apr 10
52. 52. Example 2 Solve by combining the equations ⎧7x + 2 y = 5 ⎪ ⎨ ⎪ 2x + 3 y = 16 ⎩Sun, Apr 10
53. 53. Example 2 Solve by combining the equations ⎧7x + 2 y = 5)(3) ⎪( ⎨ ⎪ 2x + 3 y = 16 ⎩Sun, Apr 10
54. 54. Example 2 Solve by combining the equations ⎧7x + 2 y = 5)(3) ⎪( ⎨ ⎪ 2x + 3 y = 16)(−2) ⎩(Sun, Apr 10
55. 55. Example 2 Solve by combining the equations ⎧7x + 2 y = 5)(3) ⎪( ⎨ ⎪ 2x + 3 y = 16)(−2) ⎩( 21x + 6 y = 15Sun, Apr 10
56. 56. Example 2 Solve by combining the equations ⎧7x + 2 y = 5)(3) ⎪( ⎨ ⎪ 2x + 3 y = 16)(−2) ⎩( 21x + 6 y = 15 −4x − 6 y = −32Sun, Apr 10
57. 57. Example 2 Solve by combining the equations ⎧7x + 2 y = 5)(3) ⎪( ⎨ ⎪ 2x + 3 y = 16)(−2) ⎩( 21x + 6 y = 15 −4x − 6 y = −32Sun, Apr 10
58. 58. Example 2 Solve by combining the equations ⎧7x + 2 y = 5)(3) ⎪( ⎨ ⎪ 2x + 3 y = 16)(−2) ⎩( 21x + 6 y = 15 −4x − 6 y = −32 17x = −17Sun, Apr 10
59. 59. Example 2 Solve by combining the equations ⎧7x + 2 y = 5)(3) ⎪( ⎨ ⎪ 2x + 3 y = 16)(−2) ⎩( 21x + 6 y = 15 −4x − 6 y = −32 17x = −17 17 17Sun, Apr 10
60. 60. Example 2 Solve by combining the equations ⎧7x + 2 y = 5)(3) ⎪( ⎨ ⎪ 2x + 3 y = 16)(−2) ⎩( 21x + 6 y = 15 −4x − 6 y = −32 17x = −17 17 17 x = −1Sun, Apr 10
61. 61. Example 2 Solve by combining the equations ⎧7x + 2 y = 5)(3) ⎪( ⎨ ⎪ 2x + 3 y = 16)(−2) ⎩( 21x + 6 y = 15 2(−1) + 3 y = 16 −4x − 6 y = −32 17x = −17 17 17 x = −1Sun, Apr 10
62. 62. Example 2 Solve by combining the equations ⎧7x + 2 y = 5)(3) ⎪( ⎨ ⎪ 2x + 3 y = 16)(−2) ⎩( 21x + 6 y = 15 2(−1) + 3 y = 16 −4x − 6 y = −32 −2 + 3 y = 16 17x = −17 17 17 x = −1Sun, Apr 10
63. 63. Example 2 Solve by combining the equations ⎧7x + 2 y = 5)(3) ⎪( ⎨ ⎪ 2x + 3 y = 16)(−2) ⎩( 21x + 6 y = 15 2(−1) + 3 y = 16 −4x − 6 y = −32 −2 + 3 y = 16 17x = −17 +2 +2 17 17 x = −1Sun, Apr 10
64. 64. Example 2 Solve by combining the equations ⎧7x + 2 y = 5)(3) ⎪( ⎨ ⎪ 2x + 3 y = 16)(−2) ⎩( 21x + 6 y = 15 2(−1) + 3 y = 16 −4x − 6 y = −32 −2 + 3 y = 16 17x = −17 +2 +2 17 17 3 y = 18 x = −1Sun, Apr 10
65. 65. Example 2 Solve by combining the equations ⎧7x + 2 y = 5)(3) ⎪( ⎨ ⎪ 2x + 3 y = 16)(−2) ⎩( 21x + 6 y = 15 2(−1) + 3 y = 16 −4x − 6 y = −32 −2 + 3 y = 16 17x = −17 +2 +2 17 17 3 y = 18 x = −1 3 3Sun, Apr 10
66. 66. Example 2 Solve by combining the equations ⎧7x + 2 y = 5)(3) ⎪( ⎨ ⎪ 2x + 3 y = 16)(−2) ⎩( 21x + 6 y = 15 2(−1) + 3 y = 16 −4x − 6 y = −32 −2 + 3 y = 16 17x = −17 +2 +2 17 17 3 y = 18 x = −1 3 3 y=6Sun, Apr 10
67. 67. Example 2 Solve by combining the equations ⎧7x + 2 y = 5)(3) ⎪( ⎨ ⎪ 2x + 3 y = 16)(−2) ⎩( Check: 21x + 6 y = 15 2(−1) + 3 y = 16 −4x − 6 y = −32 −2 + 3 y = 16 17x = −17 +2 +2 17 17 3 y = 18 x = −1 3 3 y=6Sun, Apr 10
68. 68. Example 2 Solve by combining the equations ⎧7x + 2 y = 5)(3) ⎪( ⎨ ⎪ 2x + 3 y = 16)(−2) ⎩( Check: 21x + 6 y = 15 2(−1) + 3 y = 16 −4x − 6 y = −32 7(−1) + 2(6) = 5 −2 + 3 y = 16 17x = −17 +2 +2 17 17 3 y = 18 x = −1 3 3 y=6Sun, Apr 10
69. 69. Example 2 Solve by combining the equations ⎧7x + 2 y = 5)(3) ⎪( ⎨ ⎪ 2x + 3 y = 16)(−2) ⎩( Check: 21x + 6 y = 15 2(−1) + 3 y = 16 −4x − 6 y = −32 7(−1) + 2(6) = 5 −2 + 3 y = 16 +2 −7 + 12 = 5 17x = −17 +2 17 17 3 y = 18 x = −1 3 3 y=6Sun, Apr 10
70. 70. Example 2 Solve by combining the equations ⎧7x + 2 y = 5)(3) ⎪( ⎨ ⎪ 2x + 3 y = 16)(−2) ⎩( Check: 21x + 6 y = 15 2(−1) + 3 y = 16 −4x − 6 y = −32 7(−1) + 2(6) = 5 −2 + 3 y = 16 +2 −7 + 12 = 5 17x = −17 +2 17 17 3 y = 18 2(−1) + 3(6) = 16 x = −1 3 3 y=6Sun, Apr 10
71. 71. Example 2 Solve by combining the equations ⎧7x + 2 y = 5)(3) ⎪( ⎨ ⎪ 2x + 3 y = 16)(−2) ⎩( Check: 21x + 6 y = 15 2(−1) + 3 y = 16 −4x − 6 y = −32 7(−1) + 2(6) = 5 −2 + 3 y = 16 +2 −7 + 12 = 5 17x = −17 +2 17 17 3 y = 18 2(−1) + 3(6) = 16 x = −1 3 3 −2 + 18 = 16 y=6Sun, Apr 10
72. 72. Example 2 Solve by combining the equations ⎧7x + 2 y = 5)(3) ⎪( ⎨ ⎪ 2x + 3 y = 16)(−2) ⎩( Check: 21x + 6 y = 15 2(−1) + 3 y = 16 −4x − 6 y = −32 7(−1) + 2(6) = 5 −2 + 3 y = 16 +2 −7 + 12 = 5 17x = −17 +2 17 17 3 y = 18 2(−1) + 3(6) = 16 x = −1 3 3 −2 + 18 = 16 y=6 (−1, 6)Sun, Apr 10
73. 73. Example 3 Solve by combining the equations ⎧5x + 2 y = 7 ⎪ ⎨ ⎪4x + 2 y = −3 ⎩Sun, Apr 10
74. 74. Example 3 Solve by combining the equations ⎧5x + 2 y = 7 ⎪ ⎨ ⎪4x + 2 y = −3)(−1) ⎩(Sun, Apr 10
75. 75. Example 3 Solve by combining the equations ⎧5x + 2 y = 7 ⎪ ⎨ ⎪4x + 2 y = −3)(−1) ⎩( 5x + 2 y = 7Sun, Apr 10
76. 76. Example 3 Solve by combining the equations ⎧5x + 2 y = 7 ⎪ ⎨ ⎪4x + 2 y = −3)(−1) ⎩( 5x + 2 y = 7 −4x − 2 y = 3Sun, Apr 10
77. 77. Example 3 Solve by combining the equations ⎧5x + 2 y = 7 ⎪ ⎨ ⎪4x + 2 y = −3)(−1) ⎩( 5x + 2 y = 7 −4x − 2 y = 3Sun, Apr 10
78. 78. Example 3 Solve by combining the equations ⎧5x + 2 y = 7 ⎪ ⎨ ⎪4x + 2 y = −3)(−1) ⎩( 5x + 2 y = 7 −4x − 2 y = 3 x = 10Sun, Apr 10
79. 79. Example 3 Solve by combining the equations ⎧5x + 2 y = 7 ⎪ ⎨ ⎪4x + 2 y = −3)(−1) ⎩( 5x + 2 y = 7 5(10) + 2 y = 7 −4x − 2 y = 3 x = 10Sun, Apr 10
80. 80. Example 3 Solve by combining the equations ⎧5x + 2 y = 7 ⎪ ⎨ ⎪4x + 2 y = −3)(−1) ⎩( 5x + 2 y = 7 5(10) + 2 y = 7 −4x − 2 y = 3 50 + 2 y = 7 x = 10Sun, Apr 10
81. 81. Example 3 Solve by combining the equations ⎧5x + 2 y = 7 ⎪ ⎨ ⎪4x + 2 y = −3)(−1) ⎩( 5x + 2 y = 7 5(10) + 2 y = 7 −4x − 2 y = 3 50 + 2 y = 7 −50 −50 x = 10Sun, Apr 10
82. 82. Example 3 Solve by combining the equations ⎧5x + 2 y = 7 ⎪ ⎨ ⎪4x + 2 y = −3)(−1) ⎩( 5x + 2 y = 7 5(10) + 2 y = 7 −4x − 2 y = 3 50 + 2 y = 7 −50 −50 x = 10 2 y = −43Sun, Apr 10
83. 83. Example 3 Solve by combining the equations ⎧5x + 2 y = 7 ⎪ ⎨ ⎪4x + 2 y = −3)(−1) ⎩( 5x + 2 y = 7 5(10) + 2 y = 7 −4x − 2 y = 3 50 + 2 y = 7 −50 −50 x = 10 2 y = −43 2 2Sun, Apr 10
84. 84. Example 3 Solve by combining the equations ⎧5x + 2 y = 7 ⎪ ⎨ ⎪4x + 2 y = −3)(−1) ⎩( 5x + 2 y = 7 5(10) + 2 y = 7 −4x − 2 y = 3 50 + 2 y = 7 −50 −50 x = 10 2 y = −43 2 2 −43 y= 2Sun, Apr 10
85. 85. Example 3 Solve by combining the equations ⎧5x + 2 y = 7 ⎪ ⎨ ⎪4x + 2 y = −3)(−1) ⎩( Check: 5x + 2 y = 7 5(10) + 2 y = 7 −4x − 2 y = 3 50 + 2 y = 7 −50 −50 x = 10 2 y = −43 2 2 −43 y= 2Sun, Apr 10
86. 86. Example 3 Solve by combining the equations ⎧5x + 2 y = 7 ⎪ ⎨ ⎪4x + 2 y = −3)(−1) ⎩( Check: 5x + 2 y = 7 5(10) + 2 y = 7 5(10) + 2(− ) = 7 43 −4x − 2 y = 3 50 + 2 y = 7 2 −50 −50 x = 10 2 y = −43 2 2 −43 y= 2Sun, Apr 10
87. 87. Example 3 Solve by combining the equations ⎧5x + 2 y = 7 ⎪ ⎨ ⎪4x + 2 y = −3)(−1) ⎩( Check: 5x + 2 y = 7 5(10) + 2 y = 7 5(10) + 2(− ) = 7 43 −4x − 2 y = 3 50 + 2 y = 7 2 −50 50 − 43 = 7 −50 x = 10 2 y = −43 2 2 −43 y= 2Sun, Apr 10
88. 88. Example 3 Solve by combining the equations ⎧5x + 2 y = 7 ⎪ ⎨ ⎪4x + 2 y = −3)(−1) ⎩( Check: 5x + 2 y = 7 5(10) + 2 y = 7 5(10) + 2(− ) = 7 43 −4x − 2 y = 3 50 + 2 y = 7 2 −50 50 − 43 = 7 −50 x = 10 2 y = −43 4(10) + 2(− ) = −3 43 2 2 2 −43 y= 2Sun, Apr 10
89. 89. Example 3 Solve by combining the equations ⎧5x + 2 y = 7 ⎪ ⎨ ⎪4x + 2 y = −3)(−1) ⎩( Check: 5x + 2 y = 7 5(10) + 2 y = 7 5(10) + 2(− ) = 7 43 −4x − 2 y = 3 50 + 2 y = 7 2 −50 50 − 43 = 7 −50 x = 10 2 y = −43 4(10) + 2(− ) = −3 43 2 2 2 40 − 43 = −3 −43 y= 2Sun, Apr 10
90. 90. Example 3 Solve by combining the equations ⎧5x + 2 y = 7 ⎪ ⎨ ⎪4x + 2 y = −3)(−1) ⎩( Check: 5x + 2 y = 7 5(10) + 2 y = 7 5(10) + 2(− ) = 7 43 −4x − 2 y = 3 50 + 2 y = 7 2 −50 50 − 43 = 7 −50 x = 10 2 y = −43 4(10) + 2(− ) = −3 43 2 2 2 40 − 43 = −3 −43 y= 2 (10, − ) 43 2Sun, Apr 10
91. 91. Problem SetSun, Apr 10
92. 92. Problem Set p. 350 #1-27 odd “A verbal contract isn’t worth the paper it’s written on.” - Samuel GoldwynSun, Apr 10