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Hotmath Practice Problems

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Title:
Hotmath Algebra 1
Author:
Hotmath Team
Chapter:Solving Linear SystemsSection:The Linear Combination Method (aka The Addition Method, aka the Elimination Method)
 

Problem: 1

Solve the system using linear combinations.

xy = 6

x + y = 18

 

Problem: 3

Solve the system using linear combinations.

–5x + y = 1

9x – 2y = 4

 

Problem: 5

Solve the system using linear combinations.

3x – 2y = 17

–2x – 5y = 14

 

Problem: 7

Solve the system using linear combinations.

–2u + v = 2

4u – 4v = 4

 

Problem: 9

Solve the system using linear combinations.

3m + 2n = 10

4mn = –1

 

Problem: 11

Solve the system using linear combinations. Use the graph to check your answer.

3x + y = 14

xy = –2

 

Problem: 13

Solve using linear combinations and then check your solution.

x + 4y = 4

x + 8y = 4

 

Problem: 15

Solve using linear combinations and then check your solution.

3g – 4h = 0

4g – 3h = 7

 

Problem: 17

Solve using linear combinations and then check your solution.

3a + 5z = 6

4a – 2z = 8

 

Problem: 19

Solve using linear combinations and then check your solution.

3pq = 3

3p + 4q = 28

 

Problem: 21

Solve using linear combinations and then check your solution.

x – 4y = 40

4y + x = 16

 

Problem: 23

Solve using linear combinations and then check your solution.

y = x – 8

x + 3y = 0

 

Problem: 25

Solve using linear combinations and then check your solution.

3q = 8 – 7p

8p – 18 = q

 

Problem: 27

Solve using linear combinations and then check your solution.

g – 12h = 35

20 = –g + 6h

 

Problem: 29

Tell whether addition, subtraction, or substitution would be most convenient to solve the system of equations. Then solve the system.

2xy = 5

–6x + 3y = –15

 

Problem: 31

Tell whether addition, subtraction, or substitution would be most convenient to solve the system of equations. Then solve the system.

8p + 3q = –23

8p + 14q = 10

 

Problem: 33

Tell whether addition, subtraction, or substitution would be most convenient to solve the system of equations. Then solve the system.

5x = 8 – 2y

15x = 12 – 2y

 

Problem: 35

Tell whether addition, subtraction, or substitution would be most convenient to solve the system of equations and solve the system:

 

Problem: 37

Tell whether addition, subtraction, or substitution would be most convenient to solve the system of equations. Then solve the system.

1.72x – 2.14y = –5.34

1.18x + 2.14y = 8.97

 

Problem: 39

Find two numbers with sum 82 and difference 30.