# Hotmath Practice Problems

Title:
Hotmath Algebra 1
Author:
Hotmath Team
Chapter:Solving Linear SystemsSection:Solving Linear Systems by Substitution

Problem: 1

Solve by substitution. If there is not a unique solution, state whether the system has no solution or infinitely many solutions.

y = 4x – 10

y = 5 – x

Problem: 3

Solve by substitution. If there is not a unique solution, state whether the system has no solution or infinitely many solutions.

2x + 2y = 0

6x + y = –10

Problem: 5

Solve by substitution. If there is not a unique solution, state whether the system has no solution or infinitely many solutions.

2x + 3y = 4

y = 5x – 27

Problem: 7

Solve by substitution. If there is not a unique solution, state whether the system has no solution or infinitely many solutions.

c – 3d = 2

3c + d = 16

Problem: 9

Solve by substitution. If there is not a unique solution, state whether the system has no solution or infinitely many solutions.

x + 4y = 19

x – 2y = 1

Problem: 11

Solve by substitution. If there is not a unique solution, state whether the system has no solution or infinitely many solutions.

3rs = 3

–6r + 5s = 21

Problem: 13

Solve by substitution. If there is not a unique solution, state whether the system has no solution or infinitely many solutions.

7x + 3y = 68

x – 4y = –8

Problem: 15

Solve by substitution. If there is not a unique solution, state whether the system has no solution or infinitely many solutions.

–0.5x + y = 1.5

0.8x – 0.2y = 6.0

Problem: 17

Solve by substitution. If there is not a unique solution, state whether the system has no solution or infinitely many solutions.

y = 4x – 6

Problem: 19

Solve by substitution. If there is not a unique solution, state whether the system has no solution or infinitely many solutions.

3x – 5y = 12

Problem: 21

Solve by substitution. If there is not a unique solution, state whether the system has no solution or infinitely many solutions.

Problem: 23

Solve by substitution. If there is not a unique solution, state whether the system has no solution or infinitely many solutions.

x + y = 9

y = 3x + 1

Problem: 25

Solve by substitution. If there is not a unique solution, state whether the system has no solution or infinitely many solutions.

x = y – 2

y = 10 – 3x

Problem: 27

Solve by substitution. If there is not a unique solution, state whether the system has no solution or infinitely many solutions.

y = 3x – 7

6yx = 9

Problem: 29

Solve by substitution. If there is not a unique solution, state whether the system has no solution or infinitely many solutions.

x = –4y

x = 4 – 6y

Problem: 31

Solve by substitution. If there is not a unique solution, state whether the system has no solution or infinitely many solutions.

x = 5y – 2

3xy = 8

Problem: 33

Solve by substitution. If there is not a unique solution, state whether the system has no solution or infinitely many solutions.

xy = 9

x + y = –3

Problem: 35

Solve by substitution. If there is not a unique solution, state whether the system has no solution or infinitely many solutions.

xy = 3

x + 4y = 7

Problem: 37

Solve by substitution. If there is not a unique solution, state whether the system has no solution or infinitely many solutions.

x + 3y = 25

4x + 5y = 9

Problem: 39

Solve by substitution. If there is not a unique solution, state whether the system has no solution or infinitely many solutions.

4b + 3a = 5

–3b + a = 6

Problem: 41

Solve by substitution. If there is not a unique solution, state whether the system has no solution or infinitely many solutions.

y – 3x = 0

2x + 6y = 60

Problem: 43

Solve by substitution. If there is not a unique solution, state whether the system has no solution or infinitely many solutions.

6x + 5y = 4

3x = 2 – y

Problem: 45

By substitution, solve the system of equations. Write the solution as an ordered triple of the form (x, y, z).

15xy + 6z = 108

x + z = 5

y + 4z = 2

Problem: 47

Solve the system of equations. Write the solution as an ordered triple of the form (x,y, z).

x + y + z = –25

y = –8z

x = 12z

Problem: 49

Car A costs \$10,000, and costs \$0.12 per mile to maintain. Car B costs \$11,000 and costs \$0.11 per mile to maintain. Suppose both cars are driven the same number of miles. At what mileage would the total costs of the two cars be the same?

Problem: 51

Transform the given situation to a system of equations, and solve using substitution.

Two numbers have a sum of 55 and a difference of 9. Find the numbers.

Problem: 53

Transform the given situation to a system of equations and solve.

The difference of two numbers is 10.The sum of thrice the smaller number and four times the larger is 75. Find the numbers.