Chapter 8 Practice Test Questions
Practice Test 1
1. Determine whether (6, -2) is a solution of the system.
x - y = 8
2x + 3y = 6
2. Solve by graphing.
x - y = 2
x + y = 6
Solve using the substitution method.
3. x + y = 6
y = x - 4
4. x - 2 y = 5
2x - y = 16
Solve using the addition method.
5. x + y = 12
2x - y = 6
6. 2x - y = 7
x + 2 y = 1
Solve using the addition method.
7. 2x - 3y = 8
3x + 2y = - 1
Translate to a system of equations and solve.
8. Susan is 10 years older than Matthew. In 4 years, Susan will be twice as old as Matthew. How old are they now?
9. Two cars leave town at the same time going in opposite directions. One car travels 50 mi/h and the other travels 55 mi/h. In how many hours will they be 420 miles apart?
10. A speedboat traveled 2 hours with a 4 km/h current before turning around. The return trip against the same current took 3 hours. Find the speed of the boat in still water.
11. Patrick has 15 coins, some dimes and some quarters. If their value is $2.25, how many of each does he have?
12. The sum of the digits of a two-digit number is 12. If the digits are reversed, the new number is 18 more than the original number. Find the original number.
Practice Test 2
Solve by graphing.
1. x + y = 6 and x - y = 4
2. 3x + 4y = 20 and 3x - 2y = 8
Solve using the substitution method.
3. y = 5 – x and 2x + 3y = 12
4. x + y = 6 and x + 4 y = 3
Solve using the addition method.
5. 2 x + y = 1 and x - y = 11
6. 3x - 2y = 12 and 5x + 2y = 4
Solve using the addition method.
7. 2x + 5y = 2 and 3x - 5 = 3
8. 6x + 3y = 0 and 8x + 5y = 8
Translate to a system of equations and solve.
9. Molly is 4 years younger than Heidi. In 3 years, Heidi will be twice as old as Molly. How old are they now?
10. An airplane flew for 4 hours against a head wind of 40 kdh. On the return flight the same wind was now a tail wind, and the flight took 3 hours. Find the speed of the airplane in still air.
11. A cyclist rode 3 hours with a tail wind of 6 km/h. The return trip against the head wind took 5 hours. Find the cyclist’s speed in still air.
12. A jar of nickels and dimes contains $3.30. There are 27 more nickels than dimes. How many of each are there?
13. The sum of the digits of a two-digit number is 15. If the digits are reversed, the new number is 27 less than the original number. Find the original number.
Practice Test 3
Solve by graphing.
1. x + y = 3 and x - y = 5
2. 2x + 3y = 6 and 2x – 2y = -4
Solve using the substitution method.
3. y = 3 - x and 2x + 4y = 6
4. x + y = 8 and 2x - 3y = 1
Solve using the addition method.
5. 3x + 2y = 3 and x - y = 6
6. 3~ - 7y = 16 and 5x - 7y = 36
Solve using the addition method.
7. 2x - 3y = - 1 and 3x + 4y = 24
8. 2x + 3y = 0 and 5x - 2y = - 19
Translate to a system of equations and solve.
9. Brandon is 10 years older than Brian. In 2 years, Brandon will be 3 times as old as Brian. How old are they now?
10. Two cars leave town at the same time going in opposite directions. One travels at 70 mi/h and the other at 55 mi/h. In how many hours will they be 250 miles apart?
11. Two bicyclists leave town at the same time going in the same direction. One travels at 22 km/h and the other at 38 km/h. In how many hours will they be 112 kilometers apart?
12. A jar of nickels and dimes contains $5.45. There are 8 more dimes than nickels. How many of each are there?
13. The sum of the digits of a two-digit number is 11. If the digits are reversed, the new number is 27 more than the original number. Find the original number.
Practice Test 4
Work each question carefully. Then write the letter of the best answer choice in the answer column.
1. (-4, 5) is the solution set for which of the following systems of equations?
2. Which ordered pair is the solution for the following system?
x - 3 y = 9
3x + y = 7
3. (3, 1) is the solution for the following system.
x + y = 4
2 x - y = 5
How are the graphs of the equations related?
The graphs are parallel.
The graphs coincide.
The graphs intersect at point (3, 1).
The graphs intersect at points (3, 1) and ( 1 , 3).
The substitution method can be used to solve the following system.
x + 2 y = 4
2x - 3y = 5
4. To eliminate x, which expression should you substitute for x in the second equation?
5. Which ordered pair is the solution for the system above?
6. To solve the following system by the addition method, you need to multiply the first equation by what number?
3x - y = 8
x + 5y = 2
7. In which system of equations will multiplying the first equation by -1 allow you to use the addition method?
8. Determine which system of equations represents the following problem. Two cars leave town at the same time going in the same direction. One travels at 46 mi/h, and the other travels at 53 mi/h. In how many hours will they be 35 miles apart?
9. There were 150 tickets sold for a school play. Tickets for students were $2, and tickets for adults were $3. The total amount of money collected was $340. How many more student tickets were sold than adult tickets?
10. An airplane flew for 6 hours with a tail wind of 60 km/h. The return flight against the same wind took 8 hours. Find the speed of the airplane in still air.
11. Two mopeds leave town at the same time going in opposite directions. One travels at 25 km/h and the other at 45 km/h . In how many hours will they be 210 kilometers apart?
12. A jar of nickels and dimes contains $6.75. There are 84 more nickels than dimes. How many of each are there?
13. The sum of the digits of a two-digit number is 12. If the digits are reversed, the new number is 54 more than the original number. Find the original number.
14. A collection of nickels and quarters is worth $4.65. There are 3 more nickels than quarters. How many coins are there in the collection?
Practice Test 5
Solve by graphing.
1. 3x + y = 10 and 2x - 4y = 2
2. x + y = 5 and x + y = 8
Solve using the substitution method.
3. 2 x + y = 9 and y = 3 - 4 x
4. x + y = 12 and 2x - 3y = 4
5. Translate to a system of equations and solve using the addition method.
The sum of two numbers is 88. The difference is 22. Find the numbers.
Solve using the addition method.
6. x + 2y = 6 and 3x - y = 4
7. 2x + 3y = 5 and 3x + 4y = 8
8. 1.5x - 0.5y = 4.5 and 3.0x + 1.5y = 9.0
Translate to a system of equations and solve.
9. Paul is four years younger than his brother. In four years, Paul will be three-fourths as old as his brother. How old are they now?
10. With a tail wind, a plane took 3 hours to travel 10. 1440 km. On the return trip against the same wind, the trip took an extra hour. Find the speed of the plane in still air.
11. Tickets for the school play cost $4.00 for adults and $1.50 for students. If 450 tickets were sold for a total of $925.00 on opening night, how many adult and student tickets were sold?
12. If 45 is added to a two-digit number, the result is a number with the same digits, but in reverse order. The sum of the digits is 11. What is the original number?