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Hotmath
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Hotmath
Chapter: Solving Linear Systems Section: 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 = 4 x – 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.

2 x + 2 y = 0

6 x + 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.

2 x + 3 y = 4

y = 5 x – 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 – 3 d = 2

3 c + 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 + 4 y = 19

x – 2 y = 1

 

Problem: 11

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

3 r s = 3

–6 r + 5 s = 21

 

Problem: 13

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

7 x + 3 y = 68

x – 4 y = –8

 

Problem: 15

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

–0.5 x + y = 1.5

0.8 x – 0.2 y = 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 = 4 x – 6

 

Problem: 19

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

3 x – 5 y = 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 = 3 x + 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 – 3 x

 

Problem: 27

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

y = 3 x – 7

6 y x = 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 = –4 y

x = 4 – 6 y

 

Problem: 31

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

x = 5 y – 2

3 x y = 8

 

Problem: 33

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

x y = 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.

x y = 3

x + 4 y = 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 + 3 y = 25

4 x + 5 y = 9

 

Problem: 39

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

4 b + 3 a = 5

–3 b + 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 – 3 x = 0

2 x + 6 y = 60

 

Problem: 43

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

6 x + 5 y = 4

3 x = 2 – y

 

Problem: 45

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

15 x y + 6 z = 108

x + z = 5

y + 4 z = 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 = –8 z

x = 12 z

 

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.