Practice and Problem-Solving Exercises

A Practice

See Problem 1.

Solve each system by substitution. Check your answers.

10. { 4 x + 2 y = 7 y = 5 x left brace . table with 2 rows and 1 column , row1 column 1 , 4 x plus 2 y equals 7 , row2 column 1 , y equals 5 x , end table
11. { 3 c + 2 d = 2 d = 4 left brace . table with 2 rows and 1 column , row1 column 1 , 3 c plus 2 d equals 2 , row2 column 1 , d equals 4 , end table
12. { x + 12 y = 68 x = 8 y − 12 left brace . table with 2 rows and 1 column , row1 column 1 , x plus 12 y equals 68 , row2 column 1 , x equals 8 y minus 12 , end table
13. { 4 p + 2 q = 8 q = 2 p + 1 left brace . table with 2 rows and 1 column , row1 column 1 , 4 p plus 2 q equals 8 , row2 column 1 , q equals 2 p plus 1 , end table
14. { x + 3 y = 7 2 x − 4 y = 24 left brace . table with 2 rows and 1 column , row1 column 1 , x plus 3 y equals 7 , row2 column 1 , 2 x minus 4 y equals 24 , end table
15. { x + 6 y = 2 5 x + 4 y = 36 left brace . table with 2 rows and 1 column , row1 column 1 , x plus 6 y equals 2 , row2 column 1 , 5 x plus 4 y equals 36 , end table
16. { t = 2 r + 3 5 r − 4 t = 6 left brace . table with 2 rows and 1 column , row1 column 1 , t equals 2 r plus 3 , row2 column 1 , 5 r minus 4 t equals 6 , end table
17. { y = 2 x − 1 3 x − y = − 1 left brace . table with 2 rows and 1 column , row1 column 1 , y equals 2 x minus 1 , row2 column 1 , 3 x minus y equals negative 1 , end table
18. { r + s = − 12 4 r − 6 s = 12 left brace . table with 2 rows and 1 column , row1 column 1 , r plus s equals negative 12 , row2 column 1 , 4 r minus 6 s equals 12 , end table

See Problem 2.

19. Money A student has some $1 bills and $5 bills in his wallet. He has a total of 15 bills that are worth $47. How many of each type of bill does he have?
20. A student took 60 minutes to answer a combination of 20 multiple-choice and extended-response questions. She took 2 minutes to answer each multiple-choice question and 6 minutes to answer each extended-response question.
    1. Write a system of equations to model the relationship between the number of multiple choice questions m and the number of extended-response questions r.
    2. How many of each type of question was on the test?
21. Transportation A youth group with 26 members is going skiing. Each of the five chaperones will drive a van or sedan. The vans can seat seven people, and the sedans can seat five people. Assuming there are no empty seats, how many of each type of vehicle could transport all 31 people to the ski area in one trip?

See Problem 3.

Solve each system by elimination.

22. { x + y = 12 x − y = 2 left brace . table with 2 rows and 1 column , row1 column 1 , x plus y equals 12 , row2 column 1 , x minus y equals 2 , end table
23. { x + 2 y = 10 x + y = 6 left brace . table with 2 rows and 1 column , row1 column 1 , x plus 2 y equals 10 , row2 column 1 , x plus y equals 6 , end table
24. { 3 a + 4 b = 9 − 3 a − 2 b = − 3 left brace . table with 2 rows and 1 column , row1 column 1 , 3 eh plus 4 b equals 9 , row2 column 1 , negative 3 eh minus 2 b equals negative 3 , end table
25. { 4 x + 2 y = 4 6 x + 2 y = 8 left brace . table with 2 rows and 1 column , row1 column 1 , 4 x plus 2 y equals 4 , row2 column 1 , 6 x plus 2 y equals 8 , end table
26. { 2 w + 5 y = − 24 3 w − 5 y = 14 left brace . table with 2 rows and 1 column , row1 column 1 , 2 w plus 5 y equals negative 24 , row2 column 1 , 3 w minus 5 y equals 14 , end table
27. { 3 u + 3 v = 15 − 2 u + 3 v = − 5 left brace . table with 2 rows and 1 column , row1 column 1 , 3 u plus 3 v equals 15 , row2 column 1 , negative 2 u plus 3 v equals negative 5 , end table
28. { 3 x + 2 y = 6 3 x + 3 = y left brace . table with 2 rows and 1 column , row1 column 1 , 3 x plus 2 y equals 6 , row2 column 1 , 3 x plus 3 equals y , end table
29. { 5 x − y = 4 2 x − y = 1 left brace . table with 2 rows and 1 column , row1 column 1 , 5 x minus y equals 4 , row2 column 1 , 2 x minus y equals 1 , end table
30. { 2 r + s = 3 4 r − s = 9 left brace . table with 2 rows and 1 column , row1 column 1 , 2 r plus s equals 3 , row2 column 1 , 4 r minus s equals 9 , end table

See Problems 4 and 5.

Solve each system by elimination.

31. { 4 x − 6 y = − 26 − 2 x + 3 y = 13 left brace . table with 2 rows and 1 column , row1 column 1 , 4 x minus 6 y equals negative 26 , row2 column 1 , negative 2 x plus 3 y equals 13 , end table
32. { 9 a − 3 d = 3 − 3 a + d = − 1 left brace . table with 2 rows and 1 column , row1 column 1 , 9 eh minus 3 d equals 3 , row2 column 1 , negative 3 eh plus d equals negative 1 , end table
33. { 2 a + 3 b = 12 5 a − b = 13 left brace . table with 2 rows and 1 column , row1 column 1 , 2 eh plus 3 b equals 12 , row2 column 1 , 5 eh minus b equals 13 , end table
34. { 2 x − 3 y = 6 6 x − 9 y = 9 left brace . table with 2 rows and 1 column , row1 column 1 , 2 x minus 3 y equals 6 , row2 column 1 , 6 x minus 9 y equals 9 , end table
35. { 20 x + 5 y = 120 10 x + 7.5 y = 80 left brace . table with 2 rows and 1 column , row1 column 1 , 20 x plus 5 y equals 120 , row2 column 1 , 10 x plus 7.5 y equals 80 , end table
36. { 6 x − 2 y = 11 − 9 x + 3 y = 16 left brace . table with 2 rows and 1 column , row1 column 1 , 6 x minus 2 y equals 11 , row2 column 1 , negative 9 x plus 3 y equals 16 , end table
37. { 2 x − 3 y = − 1 3 x + 4 y = 8 left brace . table with 2 rows and 1 column , row1 column 1 , 2 x minus 3 y equals negative 1 , row2 column 1 , 3 x plus 4 y equals 8 , end table
38. { 5 x − 2 y = − 19 2 x + 3 y = 0 left brace . table with 2 rows and 1 column , row1 column 1 , 5 x minus 2 y equals negative 19 , row2 column 1 , 2 x plus 3 y equals 0 , end table
39. { r + 3 s = 7 2 r − s = 7 left brace . table with 2 rows and 1 column , row1 column 1 , r plus 3 s equals 7 , row2 column 1 , 2 r minus s equals 7 , end table
40. { y = 4 − x 3 x + y = 6 left brace . table with 2 rows and 1 column , row1 column 1 , y equals 4 minus x , row2 column 1 , 3 x plus y equals 6 , end table
41. { 3 x + 2 y = 10 6 x + 4 y = 15 left brace . table with 2 rows and 1 column , row1 column 1 , 3 x plus 2 y equals 10 , row2 column 1 , 6 x plus 4 y equals 15 , end table
42. { 3 m + 4 n = − 13 5 m + 6 n = − 19 left brace . table with 2 rows and 1 column , row1 column 1 , 3 m plus 4 n equals negative 13 , row2 column 1 , 5 m plus 6 n equals negative 19 , end table

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