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Name_________________________________________________________
5.2
Date __________
Practice A
Tell which equation you would choose to solve for one of the variables
when solving the system by substitution. Explain your reasoning.
1. y  5 x  2
2 x  9 y  10
2. 3x  7 y  12
3x  12 y  6
3.
1
x y  8
5
4x  3 y  1
Solve the system of linear equations by substitution. Check your solution.
4. y  x  3
y  5x  5
5. y  3x  1
y  x7
6. x  5 y  2
x  4y  5
7. The gym has a total of 25 treadmills and stationary bikes. There are 7 more
stationary bikes than treadmills.
a. Write a system of linear equations that represents this situation.
b. How many treadmills are in the gym?
c. How many stationary bikes are in the gym?
Solve the system of linear equations by substitution. Check your solution.
8. x  y  9
2x  5 y  4
9. 2 x  3 y  25
4 x  y  15
10. 3x  6 y  2
4 x  3 y  1
11. A drawer contains 24 spoons and forks. There are three times as many
spoons as forks.
a. Write a system of linear equations that represents this situation.
b. How many spoons are in the drawer?
c. How many forks are in the drawer?
12. The perimeter of a rectangle is 34 centimeters. The length is two more than
twice the width. Write and solve a system of linear equations to find the
length and the width of the rectangle.
13. A parking lot has a total of 60 cars and trucks. The ratio of cars to trucks is
7 : 3. How many cars are in the parking lot? How many trucks are in the
parking lot? Justify your answers.
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Name _________________________________________________________ Date _________
5.2
Practice B
Solve the system of linear equations by substitution. Check your solution.
1. x  4 y  1
 3x  14  y
2. 3 y   2 x
3.
y  x5
1
x  2y  3
2
6y  1  x
4. The revenue for a vehicle rental store is $5460. There were 208 cars and
52 vans rented. A van rents for $10 more than a car.
a. Write a system of equations that represents this situation.
b. What is the cost of the car rental?
c. What is the cost of the van rental?
Solve the system of linear equations by substitution. Check your solution.
5. 2 x  y  6
x  y 1
6. 2 x  4 y   4
7. 4 x  2 y  8
x  3 y  12
6x  4 y  5
8. The sum of the digits of a two-digit number is 11. The tens digit is one less
than three times the ones digit. Find the original number.
9. The farmers’ market has a total of 98 tents. The ratio of food tents to retail
tents is 9 : 5.
a. Write a system of linear equations that represents this situation.
b. How many food tents are at the farmers’ market?
c. How many retail tents are at the farmers’ market?
10. Forty-five children attend a preschool. The number of two-year-olds is one
half the number of three-year-olds. The number of four-year-olds is the
same as the number of three-year-olds.
a. How many two-year-olds attend the preschool?
b. How many three-year-olds attend the preschool?
c. How many four-year-olds attend the preschool?
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Resources by Chapter
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All rights reserved.