(MATH 114N Week 5 Test 2 Chapter 15 Solutions)
1. Question: 15.3.29
Solve the following system by the elimination method. Check the solution.
4x – 6 = – 6y
9x + 8y = – 14
2. Question: 15.4.37
Suppose that a cyclist began a 465 mi ride across a state at the western edge of the state, at the same time that a car traveling toward it leaves the eastern end of the state, if the bicycle and car met after 7.5 hr and the car traveled 38.4 mph faster than the bicycle, find the average rate of each.
3. Question: 15.4.17
The perimeter of a standard-sized rectangular rug is 40 ft. The length is 2 ft longer than the width. Find the dimensions.
4. Question: 15.4.35
Solve the following system by the elimination method.
2x – 6y = 6
4x – 12y= 17
5. Question: 15.4.15
Building A is 200 feet shorter than Building B. The total height of the two buildings is 1500 feet. Find the height of each building.
6. Question: 15.1.15
Determine whether the given order pair is a solution of the system of equations. Remember to use alphabetically ordered variables.
(1, – 1); 3x = 2 – y
5x = 7 + 2y
7. Question: 15.1.43
Without graphing, answer the questions for the following linear system.
7x + 4y = 5
49x + 28y = 7
8. Question: 15.3.41
Solve the following system by the elimination method.
1/5 x+y= (`12)/5
1/10 x+ 1/3 y= 13/10
9. Question: 15.2.7
Solve the following system by substitution method. Check the solution.
4x + 3y = 44
x = y + 4
10 Question: 15.1.23
Solve the following system of equations by graphing.
x – 3y = 9
x + 3y = – 3
11. Question: 15.3.13
Use the elimination method to solve the following system of equations.
5x + y = – 10
7x – 3y = – 36
12. Question: 15.1.31
Solve the following system of equations by graphing. If the system is inconsistent or the equations are dependent, say so.
5x – 4y = 1
10x – 8y = 2
13. Question: 15.3.37
Solve by the elimination method.
12x + 4y = 0
– 84x – 28y = 0
14. Question: 15.3.21
Use the elimination method to solve the following system of equations.
2x – 7y = 0
4x + 4y = 0
15. Question: 15.4.13
A baseball team has home games on Wednesday and Sunday. The two games together earn $5118.50 for the team. Wednesday’s game generates $1006.50 less than Sunday’s game. How much money was taken in at each game?
16. Question: 15.3.7
Solve the following system by the elimination method.
x + y = 10
2x – y = 11
17. Question: 15.1.17
Determine whether the given order pair is a solution of the system of equations. Remember to use alphabetically ordered variables.
(9, – 6); – 3y = x + 9
3y = 8x + 54
18. Question: 15.2.13
Solve the following system by the substitution method.
5x + 8y = – 2
x + y = 2
19. Question: 15.4.33
Solve the following problem using a system of equations.
How many pounds of nuts selling for $18 per ib and raising selling for $6 per lb should a person combine to obtain 60 lb of a trail mix selling for $10 per lb?
20. Question: 15.1.15
Determine whether the given order pair is a solution of the system of equations. Remember to use alphabetically ordered variables.
(5, – 3); 3x = 18 – y
7x = 41 + 2y
21. Question: 15.2.7
Solve the following system by the substitution method. Check the solution.
5x + 4y = 33
x = y + 3
22. Question: 15.4.37
Suppose that a cyclist began a 405 mi ride across a state at the western edge of the state, at the same time that a car traveling toward it leaves the eastern end of the state, if the bicycle and car met after 7.5 hr and the car traveled 37.2 mph faster than the bicycle, find the average rate of each.
23. Question: 15.3.37
Solve by the elimination method.
6x + 3y = 0
– 18x – 9y = 0
24. Question: 15.3.41
Solve the following system by the elimination method.
1/5 x+y= (`13)/5
1/10 x+ 1/3 y= 41/30
25. Question: 15.4.33
Solve the following problem using a system of equations.
How many pounds of nuts selling for $18 per lb and raising selling for $6 per lb should a person combine to obtain 90 lb of a trail mix selling for $10 per lb?
26. Question: 15.1.31
Solve the following system of equations by graphing. If the system is inconsistent or the equations are dependent, say so.
5x – 3y = 2
15x – 9y = 6
27. Question: 15.3.7
Solve the following system by the elimination method.
x + y = 12
2x – y = 9
28. Question: 15.3.29
Solve the following system by the elimination method. Check the solution.
3x + 11 = – 5y
5x + 4y = – 12
29. Question: 15.4.13
A baseball team has home games on Wednesday and Saturday. The two games together earn $4987.50 for the team. Wednesday’s game generates $187.50 less than Sunday’s game. How much money was taken in at each game?
30. Question: 15.4.15
Building A is 150 feet shorter than Building B. The total height of the two buildings is 1490 feet. Find the height of each building.
31. Question: 15.4.17
The perimeter of a standard-sized rectangular rug is 40 ft. The length is 2 ft longer than the width. Find the dimensions.
32. Question: 15.1.43
Without graphing, answer the questions for the following linear system.
6x + 5y = 3
24x + 20y = 8
33. Question: 15.2.13
Solve the following system by the substitution method. Check the solution(s).
7x + 5y = 16
x + y = 2
34. Question: 15.1.17
Determine whether the given order pair is a solution of the system of equations. Remember to use alphabetically ordered variables. system.
(9, – 6); – 3y = x + 9
2y = 7x + 51
35. Question: 15.3.21
Use the elimination method to solve the following system of equations.
5x – 9y = 0
10x + 6y = 0
36. Question: 15.3.35
Solve the following system by the elimination method.
4x – 5y = 5
8x – 10y = 12
37. Question: 15.3.13
The elimination method to solve the following system of equations.
5x + y = – 13
7x – 3y = – 27
38. Question: 15.1.23
Solve the following system of equations by graphing.
x – 2y = 10
