See Problem 4.

Without graphing, classify each system as independent, dependent, or inconsistent.

17. { 7 x − y = 6 − 7 x + y = − 6 left brace . table with 2 rows and 1 column , row1 column 1 , 7 x minus y equals 6 , row2 column 1 , negative 7 x plus y equals negative 6 , end table
18. { − 3 x + y = 4 x − 1 3 y = 1 left brace . table with 2 rows and 1 column , row1 column 1 , negative 3 x plus y equals 4 , row2 column 1 , x minus , 1 third , y equals 1 , end table
19. { 4 x + 8 y =   12 x + 2 y = − 3 left brace . table with 2 rows and 1 column , row1 column 1 , 4 x plus 8 y equals 12 , row2 column 1 , x plus 2 y equals negative 3 , end table
20. { y = 2 x − 1 y = − 2 x + 5 left brace . table with 2 rows and 1 column , row1 column 1 , y equals 2 x minus 1 , row2 column 1 , y equals negative 2 x plus 5 , end table
21. { x = 6 y = − 2 left brace . table with 2 rows and 1 column , row1 column 1 , x equals 6 , row2 column 1 , y equals negative 2 , end table
22. { 2 y = 5 x + 6 − 10 x + 4 y = 8 left brace . table with 2 rows and 1 column , row1 column 1 , 2 y equals 5 x plus 6 , row2 column 1 , negative 10 x plus 4 y equals 8 , end table
23. { x − 3 y = 2 4 x − 12 y = 8 left brace . table with 2 rows and 1 column , row1 column 1 , x minus 3 y equals 2 , row2 column 1 , 4 x minus 12 y equals 8 , end table
24. { y − x = 0 y = − x left brace . table with 2 rows and 1 column , row1 column 1 , y minus x equals 0 , row2 column 1 , y equals negative x , end table
25. { 2 y − x = 4 1 2 x + y = 2 left brace . table with 2 rows and 1 column , row1 column 1 , 2 y minus x equals 4 , row2 column 1 , 1 half , x plus y equals 2 , end table
26. { x + 4 y = 12 2 x − 8 y = 4 left brace . table with 2 rows and 1 column , row1 column 1 , x plus 4 y equals 12 , row2 column 1 , 2 x minus 8 y equals 4 , end table
27. { 4 x + 8 y = − 6 6 x + 12 y = − 9 left brace . table with 2 rows and 1 column , row1 column 1 , 4 x plus 8 y equals negative 6 , row2 column 1 , 6 x plus 12 y equals negative 9 , end table
28. { 4 y − 2 x = 6 8 y = 4 x − 12 left brace . table with 2 rows and 1 column , row1 column 1 , 4 y minus 2 x equals 6 , row2 column 1 , 8 y equals 4 x minus 12 , end table

B Apply

Graph and solve each system.

29. { 3 = 4 y + x 4 y = − x + 3 left brace . table with 2 rows and 1 column , row1 column 1 , 3 equals 4 y plus x , row2 column 1 , 4 y equals negative x plus 3 , end table
30. { y = 1 2 x + 1 2 y = 1 4 x + 3 2 left brace . table with 2 rows and 1 column , row1 column 1 , y equals , 1 half , x plus , 1 half , row2 column 1 , y equals , 1 fourth , x plus , 3 halves , end table
31. { 3 x + 6 y − 12 = 0 x + 2 y = 8 left brace . table with 2 rows and 1 column , row1 column 1 , 3 x plus 6 y minus 12 equals 0 , row2 column 1 , x plus 2 y equals 8 , end table
32. { y = − 3 x + 3 y = 2 x − 7 left brace . table with 2 rows and 1 column , row1 column 1 , y equals negative 3 x plus 3 , row2 column 1 , y equals 2 x minus 7 , end table
33. { 3 x = − 5 y + 4 250 + 150 x = 300 y left brace . table with 2 rows and 1 column , row1 column 1 , 3 x equals negative 5 y plus 4 , row2 column 1 , 250 plus 150 x equals 300 y , end table
34. { x + 3 y = 6 6 y + 2 x = 12 left brace . table with 2 rows and 1 column , row1 column 1 , x plus 3 y equals 6 , row2 column 1 , 6 y plus 2 x equals 12 , end table
35. { − x + 3 y = 6 2 x − y = 8 left brace . table with 2 rows and 1 column , row1 column 1 , negative x plus 3 y equals 6 , row2 column 1 , 2 x minus y equals 8 , end table
36. { y = − 1 2 x + 8 y = 2 x − 6 left brace . table with 2 rows and 1 column , row1 column 1 , y equals negative , 1 half , x plus 8 , row2 column 1 , y equals 2 x minus 6 , end table
37. { y = − 2 x + 6 x − 3 y = − 6 left brace . table with 2 rows and 1 column , row1 column 1 , y equals negative 2 x plus 6 , row2 column 1 , x minus 3 y equals negative 6 , end table

Without graphing, classify each system as independent, dependent, or inconsistent.

38. { 3 x − 2 y = 8 4 y = 6 x − 5 left brace . table with 2 rows and 1 column , row1 column 1 , 3 x minus 2 y equals 8 , row2 column 1 , 4 y equals 6 x minus 5 , end table
39. { 2 x + 8 y = 6 x = − 4 y + 3 left brace . table with 2 rows and 1 column , row1 column 1 , 2 x plus 8 y equals 6 , row2 column 1 , x equals negative 4 y plus 3 , end table
40. { 3 m = − 5 n + 4 n − 6 5 = − 3 5 m left brace . table with 2 rows and 1 column , row1 column 1 , 3 m equals negative 5 n plus 4 , row2 column 1 , n minus , 6 fifths , equals negative , 3 fifths , m , end table
41. Think About a Plan You and a friend are both reading a book. You read 2 pages each minute and have already read 55 pages. Your friend reads 3 pages each minute and has already read 35 pages. Graph and solve a system of equations to find when the two of you will have read the same number of pages. Since the number of pages you have read depends on how long you have been reading, let x represent the number of minutes it takes to read y pages.
    • How can you describe the relationship between x and y for you?
    • How can you describe the relationship between x and y for your friend?
    • How can a graph help you solve this problem?
42. Sports You can choose between two tennis courts at two university campuses to learn how to play tennis. One campus charges $25 per hour. The other campus charges $20 per hour plus a one-time registration fee of $10.
    1. Write a system of equations to represent the cost c for h hours of court use at each campus.
    2. Graphing Calculator Find the number of hours for which the costs are the same.
    3. Reasoning If you want to practice for a total of 10 hours, which university campus should you choose? Explain.

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