Download Determine the best method to solve each system of equations. Then

6-5 Applying Systems of Linear Equations
Determine the best method to solve each system of equations. Then solve the system.
6. −3x + y = −3
4x + 2y = 14
SOLUTION: The coefficient of y in one of the equations is 1, so solve the system by substitution.
First, solve equation 1 for y. Substitute into equation 2. Now, substitute 2 for x in either equation to find the value of y.
The solution is (2, 3).
9. 5x + 8y = 1
−2x + 8y = −6
SOLUTION: The coefficients for y are the same. Solve the system by elimination using subtraction.
Now, substitute 1 for x in either equation to find the value of y.
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6-5 Applying
Systems
The solution
is (2, 3).of Linear Equations
9. 5x + 8y = 1
−2x + 8y = −6
SOLUTION: The coefficients for y are the same. Solve the system by elimination using subtraction.
Now, substitute 1 for x in either equation to find the value of y.
The solution is
.
12. FINANCIAL LITERACY For a Future Teachers of America fundraiser, Denzell sold food as shown in the table.
He sold 11 more subs than pizzas and earned a total of $233. Write and solve a system of equations to represent this
situation. Then describe what the solution means.
SOLUTION: Let s represent the number of subs sold and p represent the number of pizzas sold.
3s + 5p = 233; s = p + 11
Solve through substitution.
Now, substitute 25 for p in either equation to find the value of s.
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6-5 Applying Systems of Linear Equations
The solution is
.
12. FINANCIAL LITERACY For a Future Teachers of America fundraiser, Denzell sold food as shown in the table.
He sold 11 more subs than pizzas and earned a total of $233. Write and solve a system of equations to represent this
situation. Then describe what the solution means.
SOLUTION: Let s represent the number of subs sold and p represent the number of pizzas sold.
3s + 5p = 233; s = p + 11
Solve through substitution.
Now, substitute 25 for p in either equation to find the value of s.
Denzell sold 25 pizzas and 36 subs.
15. CCSS MODELING The break-even point is the point at which income equals expenses. Ridgemont High School
is paying $13,200 for the writing and research of their yearbook plus a printing fee of $25 per book. If they sell the
books for $40 each, how many will they have to sell to break even? Explain.
SOLUTION: Let b represent the number of books they have to sell and p represent the break-even point.
13,200 + 25b = p ; 40b = p
Solve through substitution.
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Now, substitute 880 for b in either equation to find the value of p .
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6-5 Applying
Systems of Linear Equations
Denzell sold 25 pizzas and 36 subs.
15. CCSS MODELING The break-even point is the point at which income equals expenses. Ridgemont High School
is paying $13,200 for the writing and research of their yearbook plus a printing fee of $25 per book. If they sell the
books for $40 each, how many will they have to sell to break even? Explain.
SOLUTION: Let b represent the number of books they have to sell and p represent the break-even point.
13,200 + 25b = p ; 40b = p
Solve through substitution.
Now, substitute 880 for b in either equation to find the value of p .
The school needs to sell 880 books to break even. If they sell this number, then their income and expenses both equal
$35,200.
16. PAINTBALL Clara and her friends are planning a trip to a paintball park. Find the cost of lunch and the cost of
each paintball. What would be the cost for 400 paintballs and lunch?
SOLUTION: Let l represent the cost of lunch and p represent the cost of each paintball.
500p + l =25; 200p + l = 16
Solve through elimination by subtraction.
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Now, substitute 0.3 for p in either equation to find the value of l.
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The schoolSystems
needs toof
sell
880 books
to break even. If they sell this number, then their income and expenses both equal
6-5 Applying
Linear
Equations
$35,200.
16. PAINTBALL Clara and her friends are planning a trip to a paintball park. Find the cost of lunch and the cost of
each paintball. What would be the cost for 400 paintballs and lunch?
SOLUTION: Let l represent the cost of lunch and p represent the cost of each paintball.
500p + l =25; 200p + l = 16
Solve through elimination by subtraction.
Now, substitute 0.3 for p in either equation to find the value of l.
The cost of 400 paintballs and lunch would be:
The cost of the lunch is $10 and the cost of each paintball is $0.03. The cost of 400 paintballs and lunch would be $22.
18. BOOKS The library is having a book sale. Hardcover books sell for $4 each, and paperback books are $2 each. If
Connie spends $26 for 8 books, how many hardcover books did she buy?
SOLUTION: Let h represent the number of hardcover books and p represent the number of paperback books Connie bought.
4h + 2p = 26; h + p = 8
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Solve through substitution.
First, solve for p in equation 2. Page 5
6-5 Applying
Systems of Linear Equations
The cost of the lunch is $10 and the cost of each paintball is $0.03. The cost of 400 paintballs and lunch would be $22.
18. BOOKS The library is having a book sale. Hardcover books sell for $4 each, and paperback books are $2 each. If
Connie spends $26 for 8 books, how many hardcover books did she buy?
SOLUTION: Let h represent the number of hardcover books and p represent the number of paperback books Connie bought.
4h + 2p = 26; h + p = 8
Solve through substitution.
First, solve for p in equation 2. Substitute in equation 1. Connie bought 5 hardcover books.
21. OPEN ENDED Formulate a system of equations that represents a situation in your school. Describe the method
that you would use to solve the system. Then solve the system and explain what the solution means.
SOLUTION: Sample answer: x + y = 12 and 3x + 2y = 29, where x represents the cost of a student ticket for the basketball game
and y represents the cost of an adult ticket; substitution could be used to solve the system; (5, 7) means the cost of a
student ticket is $5 and the cost of an adult ticket is $7.
24. WRITE A QUESTION A classmate says that elimination is the best way to solve a system of equations. Write a
question to challenge his conjecture.
SOLUTION: Sample answer: Would another method work better if one of the equations is in the form y = mx + b?
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