Solved Examples and Worksheet for Writing and Solving Systems of Linear Equations

Q1Josh bought 28 soaps and shampoo bottles for $174. Cost of one soap is $3and cost of one shampoo bottle is $10. Let x be the number of soaps and y be the number of shampoo bottles. Identify the linear system of equations that represent the situation.
A. x + y = 28 and 10x + 3y = 174
B. x + y = 28 and 3x + 10y = 174
C. x + y = 174 and 10x + 3y = 28
D. x + y = 174 and 3x + 10y = 28

Solutions
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Step: 1
x + y = 28
  [Total number of soaps and shampoo bottles is 28.]
Step: 2
Cost of x soaps = $3x
  [Cost of a soap = $3.]
Step: 3
Cost of y shampoo bottles = $10y
  [Cost of a shampoo bottle is $10.]
Step: 4
Cost of 28 soaps and shampoo bottles is $174. So, 3x + 10y = 174
Step: 5
So, the system of equations are x + y = 28 and 3x + 10y = 174.
Correct Answer is :   x + y = 28 and 3x + 10y = 174
Q2James bought 12 candies and cookies for $11. The cost of a candy is $1 and the cost of a cookie is $0.8. Let x be the number of candies and y be the number of cookies. Which system of linear equations represents the situation?
A. x + y = 11, x + 0.8y = 12
B. x + y = 11, x + 0.8y = 12
C. x + y = 12, 0.8x + y = 11
D. x + y = 12, x + 0.8y = 11

Solutions
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Step: 1
x + y = 12.
  [Total number of candies and cookies = 12.]
Step: 2
Cost of x candies is $x
  [Cost of a candy = $1.]
Step: 3
Cost of y cookies is $0.8y.
  [Cost of a candy = $0.8.]
Step: 4
Cost of 12 candies and cookies is $11, so x + 0.8y = 11.
  [Total cost = $11.]
Step: 5
The required system of equation is x + y = 12, x + 0.8y = 11.
Correct Answer is :   x + y = 12, x + 0.8y = 11
Q3Rafael bought two types of movie tickets at $6 and $8 for 9 of his friends. Total cost of the tickets is $60. Let x be the number of $6 tickets and y be the number of $8 tickets. Which system of linear equations represents the situation?
A. x + y > 9, 8x + 6y = 60
B. x + y = 9, 8x + 6y = 60
C. x + y = 9, 6x + 8y = 60
D. x + y < 9, 6x + 8y = 60

Solutions
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Step: 1
x + y = 9
  [Total number of tickets = 9.]
Step: 2
Cost of x tickets is 6x.
Step: 3
Cost of y tickets is 8y.
Step: 4
Cost of 9 tickets is $60, so 6x + 8y = 60.
  [Total cost = $60.]
Step: 5
The required system of equation is x + y = 9, 6x + 8y = 60.
Correct Answer is :   x + y = 9, 6x + 8y = 60
Q4Three soccer balls and two baseballs cost $28. Two soccer balls and four baseballs cost $36. Which system of linear equations represents the situation?

A. 4x + 2y = 28, 2x + 3y = 36
B. 2x + 3y = 28, x + 4y = 36
C. 3x + 2y = 36, 2x + 4y = 28
D. 3x + 2y = 28, 2x + 4y = 36

Solutions
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Step: 1
The equation '3x + 2y = 28' represents the situation 'Three soccer balls and two baseballs cost $28'.
Step: 2
The equation '2x + 4y = 36' represents the situation 'Two soccer balls and four baseballs cost $36'.
Step: 3
So, '3x + 2y = 28 and 2x + 4y = 36' is the system of linear equations that represents the given situation.
Correct Answer is :   3x + 2y = 28, 2x + 4y = 36
Q5One glass of lemonade and two hamburgers cost $10. Three glasses of lemonade and four hamburgers cost $24. Which system of linear equations represents the situation?

A. 2x + y = 10, 4x + 3y = 24
B. 3x + 2y = 10, x + 4y = 24
C. x + 2y = 10, 3x + 4y = 24
D. x + 2y = 24, 3x + 4y = 10

Solutions
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Step: 1
The equation 'x + 2y = 10' represents the situation 'one glass of lemonade and two hamburgers cost $10'.
Step: 2
The equation ' 3x + 4y = 24' represents the situation 'three glasses of lemonade and four hamburgers cost $24'.
Step: 3
So, 'x + 2y = 10 and 3x + 4y = 24' is the system of linear equations that represents the given situation.
Correct Answer is :   x + 2y = 10, 3x + 4y = 24
Q6Four bars of soap and 3 mirrors cost $12. Two bars of soap and 5 mirrors cost $16. Which system of linear equations represents the situation?

A. 4x + 3y = 16, 2x + 5y = 12
B. 4x + 3y = 12, 2x + 5y = 16
C. 3x + 4y = 12, 5x + 2y = 16
D. 3x + 4y = 16, 5x + 2y = 12

Solutions
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Step: 1
The equation '4x + 3y = 12' represents the situation 'four bars of soap and 3 mirrors cost $12'.
Step: 2
The equation '2x + 5y = 16' represents the situation 'two bars of soap and 5 mirrors cost $16'.
Step: 3
So, '4x + 3y = 12 and 2x + 5y = 16' is the system of linear equations that represents the given sitution.
Correct Answer is :   4x + 3y = 12, 2x + 5y = 16
Q7Three baseball bats and 5 tennis rackets cost $99. Two baseball bats and 1 tennis racket cost $35. Which system of linear equations represents the situation?

A. 3x + 5y = 99, 2x + y = 35
B. 3x + 5y = 35, 2x + y = 99
C. 5x + 3y = 99, x + 2y = 35
D. 5x + 3y = 35, x + 2y = 99

Solutions
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Step: 1
The equation '3x + 5y = 99' represents the situation ' three baseball bats and 5 tennis ractkets cost $99.
Step: 2
The equation '2x +y = 35' represents the situation 'two baseball bats and 1 tennis racket cost $35.
Step: 3
So, '3x + 5y = 99 and 2x + y = 35' is the system of linear equations that represents the given situation.
Correct Answer is :   3x + 5y = 99, 2x + y = 35
Q8The cost of an apple is $0.8 and that of an orange is $0.5. Justin purchased 20 fruits for $13. If x represents the number of apples and y the number of oranges, which system of linear equations represents the situation?
A. x + y = 13, 0.5x + 0.8y = 20
B. x + y = 13, 0.8x + 0.5y = 20
C. x + y = 20, 0.5x + 0.8y = 13
D. x + y = 20, 0.8x + 0.5y = 13

Solutions
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Step: 1
x + y = 20
  [Total number of fruits = 20.]
Step: 2
Cost of x apples is $0.8x.
  [Cost of an apple = $0.8.]
Step: 3
Cost of y orange is $0.5y.
  [Cost of an orange = $0.5.]
Step: 4
Cost of 20 fruits is $13, so 0.8x + 0.5y = 13
  [Total cost = $13.]
Step: 5
The required system of equations is x + y = 20, 0.8x + 0.5y = 13.
Correct Answer is :   x + y = 20, 0.8x + 0.5y = 13

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