1. Section 3.2

2. 1.Solve one of the equations for one of its variables. 2.Substitute the expression for #1 into the other equation and solve for the other variable. 3.Substitute the value from #2 into the equation from #1 and solve. Substitution Method

3. Solve each system of equations using substitution. Write your answer as an ordered pair. Examples

4. 2x + 2x + 3 = 7y = 2(1) + 3 4x + 3 = 7= 2 + 3 4x = 4= 5 x = 1(1, 5)

5. 2x + 5(2x) = −12y = 2(−1) 2x + 10x = −12= −2 12x = −12(−1, −2) x = −1

6. 2y + 1 + 3y = 11x = 2(2) + 1 5y + 1 = 11= 4 + 1 5y = 10= 5 y = 2(5, 2)

7. 2y – (3y – 5) = 10x = 3(−5) – 5 2y – 3y + 5 = 10= −15 – 5 −y + 5 = 10= −20 −y = 5(−20, −5) y = −5

8. 2(−4x + 5) = −3x2y = −3(2) −8x + 10 = −3x2y = −6 10 = 5xy = −3 x = 2(2, −3)

9. 3x – (3x – 7) = 7 3x – 3x + 7 = 7 7 = 7 True Infinitely Many Solutions

10. 2(−x + 3) + 2x = 4 −2x + 6 + 2x = 4 6 = 4 False No Solution

11. x – y = –4 x = y – 4 6(y – 4) + 2y = 8x = 4 – 4 6y – 24 + 2y = 8= 0 8y – 24 = 8(0, 4) 8y = 32 y = 4

12. Elimination Method

13. 1.Multiply one or both of the equations by a constant to obtain coefficients that differ only in sign for one of the variables. 2.Add the revised equations from #1. Combining like terms will eliminate one of the variables. Solve for the remaining variable. 3.Substitute the value obtained in #2 into either of the original equations and solve for the other variable.

14. Solve each system of equations using elimination. Write your answer as an ordered pair. Examples

15. 7x7x= 14 x = 2 4(2) + 2y = 10 8 + 2y = 10 2y = 2 y = 1 (2, 1)

16. 3x + 6(3) = 18 3x + 18 = 18 3x = 0 x = 0 (0, 3) 10y = 30 y = 3

17. 2 + 2b = −4 2b = −6 b = −3 (2, −3) 2 5a5a a = 2 = 10

18. 4(2) + 3b = −1 8+ 3b = −1 3b = −9 b = −3 (2, −3) −2 −3a a = 2 = −6

19. 5(−1) – n = 1 −5 – n = 1 −n = 6 n = −6 (−1, −6) −3 −9m m = −1 = 9

20. 3x + 5(1) = 11 3x + 5 = 11 3x = 6 x = 2 (2, 1) 2 −3 y = 1

21. 3u + 7(2) = 23 3u + 14 = 23 3u = 9 u = 3 (3, 2) 2 3 38v = 76 v = 2

22. 3a + 2(−3) = 6 3a – 6 = 6 3a = 12 a = 4 (4, −3) 4 −3 −b = 3 b = −3

23. Application Problems

24. a) Define the unknowns. b) Set of the system of equations. c) Solve the system of equations. d) Write a sentence to answer the question. Examples

25. 1. The perimeter of a rectangular garden is 40 meters. The length of the garden is 1 meter less than twice its width. Find the dimensions. a)Let x = width Let y = length b)

26. 2x + 2(2x – 1) = 40 2x + 4x – 2 = 40 6x – 2 = 40 6x = 42The dimension of the x = 7rectangle are 7 meters by y = 2(7) – 1 13 meters. = 14 – 1 = 13

27. 2. Six boxes of apples and 5 boxes of grapefruits cost $142. At the same time 3 boxes of apples and 2 boxes of grapefruits cost $64. Find the cost of one box of each. a)Let a = the cost of a box of apples Let g = the cost of a box of grapefruits b)

28. The cost of a box of apples is $12 and the cost of a box of grapefruits is $14. −2 g = 14 3a + 2(14) = 64 3a + 28 = 64 3a = 36 a = 12

29. 3. During a special promotion, Southern Air issued round-trip first-class tickets from Orlando to Dallas at $225, and coach tickets at $198. If 167 tickets were purchased for at total price of $35,172, how many of each ticket were sold. a)Let f = the # of a first-class tickets sold Let c = the # of a coach tickets sold b)

30. 78 first-class tickets were sold and 89 coach ticket were sold. 225(167 – c) + 198c = 35,172 37,575 – 225c + 198c = 35,172 37,575 – 27c = 35,172 −27c = −2403 c = 89 f = 167 – 89 = 78