SYSTEMS OF EQUATIONS
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Last updated 11 months ago
47 questions
Note from the author:
SYSTEMS OF EQUATIONS FROM JMAP
1
A system of equations is shown below. Which method eliminates one of the variables?
- Equation A: 5x + 9y = 12
- Equation B: 4x - 3y = 8
A system of equations is shown below. Which method eliminates one of the variables?
- Equation A: 5x + 9y = 12
- Equation B: 4x - 3y = 8
1
Using the substitution method, Vito is solving the following system of equations algebraically. Which equivalent equation could Vito use?
- Equations:
- y + 3x = -4
- 2x - 3y = -21
Using the substitution method, Vito is solving the following system of equations algebraically. Which equivalent equation could Vito use?
- Equations:
- y + 3x = -4
- 2x - 3y = -21
1
Which system of equations has the same solution as the system below?
- System:
- 2x + 2y = 16
- 3x - y = 4
Which system of equations has the same solution as the system below?
- System:
- 2x + 2y = 16
- 3x - y = 4
1
Which pair of equations could not be used to solve the following equations for x and y?
- Equations:
- 4x + 2y = 22
- -2x + 2y = -8
Which pair of equations could not be used to solve the following equations for x and y?
- Equations:
- 4x + 2y = 22
- -2x + 2y = -8
1
A system of equations is given below. Which system of equations does not have the same solution?
- Given system:
- x + 2y = 5
- 2x + y = 4
A system of equations is given below. Which system of equations does not have the same solution?
- Given system:
- x + 2y = 5
- 2x + y = 4
1
Which system of equations does *not* have the same solution as the system below?
- System:
\[
\begin{align*}
4x + 3y &= 10 \\
-6x - 5y &= -16
\end{align*}
\]
- Choices:
Which system of equations does *not* have the same solution as the system below?
- System:
\[
\begin{align*}
4x + 3y &= 10 \\
-6x - 5y &= -16
\end{align*}
\]
- Choices:
1
Which system of equations will yield the same solution as the system below?
- System:
\[
\begin{align*}
x - y &= 3 \\
2x - 3y &= -1
\end{align*}
\]
- Choices:
Which system of equations will yield the same solution as the system below?
- System:
\[
\begin{align*}
x - y &= 3 \\
2x - 3y &= -1
\end{align*}
\]
- Choices:
1
Which system of linear equations has the same solution as the one shown below?
- System:
\[
\begin{align*}
x - 4y &= -10 \\
x + y &= 5
\end{align*}
\]
- Choices:
Which system of linear equations has the same solution as the one shown below?
- System:
\[
\begin{align*}
x - 4y &= -10 \\
x + y &= 5
\end{align*}
\]
- Choices:
1
Which system of equations has the same solutions as the system below?
- System:
\[
\begin{align*}
3x - y &= 7 \\
2x + 3y &= 12
\end{align*}
\]
- Choices:
Which system of equations has the same solutions as the system below?
- System:
\[
\begin{align*}
3x - y &= 7 \\
2x + 3y &= 12
\end{align*}
\]
- Choices:
1
Last week, a candle store received $355.60 for selling 20 candles. Small candles sell for $10.98 and large candles sell for $27.98. How many large candles did the store sell?
Last week, a candle store received $355.60 for selling 20 candles. Small candles sell for $10.98 and large candles sell for $27.98. How many large candles did the store sell?
1
Two friends went to a restaurant and ordered one plain pizza and two sodas. Their bill totaled $15.95. Later that day, five friends went to the same restaurant. They ordered three plain pizzas and each person had one soda. Write and solve a system of equations to determine the price of one plain pizza. [Only an algebraic solution can receive full credit.]
Two friends went to a restaurant and ordered one plain pizza and two sodas. Their bill totaled $15.95. Later that day, five friends went to the same restaurant. They ordered three plain pizzas and each person had one soda. Write and solve a system of equations to determine the price of one plain pizza. [Only an algebraic solution can receive full credit.]
1
There are two parking garages in Beacon Falls. Garage A charges $7.00 to park for the first 2 hours, and each additional hour costs $3.00. Garage B charges $3.25 per hour to park. When a person parks for at least 2 hours, write equations to model the cost of parking for a total of x hours in Garage A and Garage B. Determine algebraically the number of hours when the cost of parking at both garages will be the same.
There are two parking garages in Beacon Falls. Garage A charges $7.00 to park for the first 2 hours, and each additional hour costs $3.00. Garage B charges $3.25 per hour to park. When a person parks for at least 2 hours, write equations to model the cost of parking for a total of x hours in Garage A and Garage B. Determine algebraically the number of hours when the cost of parking at both garages will be the same.
1
A fence was installed around the edge of a rectangular garden. The length, l, of the fence was 5 feet less than 3 times its width, w. The amount of fencing used was 90 feet. Write a system of equations or write an equation using one variable that models this situation. Determine algebraically the dimensions, in feet, of the garden.
A fence was installed around the edge of a rectangular garden. The length, l, of the fence was 5 feet less than 3 times its width, w. The amount of fencing used was 90 feet. Write a system of equations or write an equation using one variable that models this situation. Determine algebraically the dimensions, in feet, of the garden.
1
An animal shelter spends $2.35 per day to care for each cat and $5.50 per day to care for each dog. Pat noticed that the shelter spent $89.50 caring for cats and dogs on Wednesday. Write an equation to represent the possible numbers of cats and dogs that could have been at the shelter on Wednesday. Pat said that there might have been 8 cats and 14 dogs at the shelter on Wednesday. Are Pat’s numbers possible? Use your equation to justify your answer. Later, Pat found a record showing that there were a total of 22 cats and dogs at the shelter on Wednesday. How many cats were at the shelter on Wednesday?
An animal shelter spends $2.35 per day to care for each cat and $5.50 per day to care for each dog. Pat noticed that the shelter spent $89.50 caring for cats and dogs on Wednesday. Write an equation to represent the possible numbers of cats and dogs that could have been at the shelter on Wednesday. Pat said that there might have been 8 cats and 14 dogs at the shelter on Wednesday. Are Pat’s numbers possible? Use your equation to justify your answer. Later, Pat found a record showing that there were a total of 22 cats and dogs at the shelter on Wednesday. How many cats were at the shelter on Wednesday?
1
Jacob and Zachary go to the movie theater and purchase refreshments for their friends. Jacob spends a total of $18.25 on two bags of popcorn and three drinks. Zachary spends a total of $27.50 for four bags of popcorn and two drinks. Write a system of equations that can be used to find the price of one bag of popcorn and the price of one drink. Using these equations, determine and state the price of a bag of popcorn and the price of a drink, to the nearest cent.
Jacob and Zachary go to the movie theater and purchase refreshments for their friends. Jacob spends a total of $18.25 on two bags of popcorn and three drinks. Zachary spends a total of $27.50 for four bags of popcorn and two drinks. Write a system of equations that can be used to find the price of one bag of popcorn and the price of one drink. Using these equations, determine and state the price of a bag of popcorn and the price of a drink, to the nearest cent.
1
For a class picnic, two teachers went to the same store to purchase drinks. One teacher purchased 18 juice boxes and 32 bottles of water and spent $19.92. The other teacher purchased 14 juice boxes and 26 bottles of water and spent $15.76. Write a system of equations to represent the costs of a juice box, j, and a bottle of water, w. Kara said that the juice boxes might have cost 52 cents each and that the bottles of water might have cost 33 cents each. Use your system of equations to justify that Kara's prices are not possible. Solve your system of equations to determine the actual cost, in dollars, of each juice box and each bottle of water.
For a class picnic, two teachers went to the same store to purchase drinks. One teacher purchased 18 juice boxes and 32 bottles of water and spent $19.92. The other teacher purchased 14 juice boxes and 26 bottles of water and spent $15.76. Write a system of equations to represent the costs of a juice box, j, and a bottle of water, w. Kara said that the juice boxes might have cost 52 cents each and that the bottles of water might have cost 33 cents each. Use your system of equations to justify that Kara's prices are not possible. Solve your system of equations to determine the actual cost, in dollars, of each juice box and each bottle of water.
1
At Bea's Pet Shop, the number of dogs \( d \) is initially five less than twice the number of cats \( c \). If she decides to add three more of each, the ratio of cats to dogs will be \( \frac{3}{4} \). Write an equation or system of equations to find the number of cats and dogs Bea has in her pet shop.
At Bea's Pet Shop, the number of dogs \( d \) is initially five less than twice the number of cats \( c \). If she decides to add three more of each, the ratio of cats to dogs will be \( \frac{3}{4} \). Write an equation or system of equations to find the number of cats and dogs Bea has in her pet shop.
1
Could Bea's Pet Shop initially have 15 cats and 20 dogs? Explain your reasoning.
Could Bea's Pet Shop initially have 15 cats and 20 dogs? Explain your reasoning.
1
Determine algebraically the number of cats and dogs Bea initially had in her pet shop.
Determine algebraically the number of cats and dogs Bea initially had in her pet shop.
1
Dylan has a bank that sorts coins as they are dropped into it. A panel on the front displays the total number of coins inside as well as the total value of these coins. The panel shows 90 coins with a value of $17.55 inside of the bank. If Dylan only collects dimes and quarters: Write a system of equations in two variables or an equation in one variable that could model this situation.
Dylan has a bank that sorts coins as they are dropped into it. A panel on the front displays the total number of coins inside as well as the total value of these coins. The panel shows 90 coins with a value of $17.55 inside of the bank. If Dylan only collects dimes and quarters: Write a system of equations in two variables or an equation in one variable that could model this situation.
1
Using your equation or system of equations, determine the number of quarters Dylan has in his bank.
Using your equation or system of equations, determine the number of quarters Dylan has in his bank.
1
Dylan's mom told him she would replace each one of his dimes with a quarter. Determine if Dylan would then have enough money to buy a game priced at $20.98 with an 8% sales tax. Justify your answer.
Dylan's mom told him she would replace each one of his dimes with a quarter. Determine if Dylan would then have enough money to buy a game priced at $20.98 with an 8% sales tax. Justify your answer.
1
At the present time, Mrs. Bee's age is six years more than four times her son's age. Three years ago, she was seven times as old as her son was then. If \( b \) represents Mrs. Bee's age now and \( s \) represents her son's age now: Write a system of equations that could model this scenario.
At the present time, Mrs. Bee's age is six years more than four times her son's age. Three years ago, she was seven times as old as her son was then. If \( b \) represents Mrs. Bee's age now and \( s \) represents her son's age now: Write a system of equations that could model this scenario.
1
Use this system of equations to determine, algebraically, the ages of both Mrs. Bee and her son now.
Use this system of equations to determine, algebraically, the ages of both Mrs. Bee and her son now.
1
Determine how many years from now Mrs. Bee will be three times as old as her son will be then.
Determine how many years from now Mrs. Bee will be three times as old as her son will be then.
1
Two families went to a fast-food restaurant in a state with no sales tax. The Browns bought 4 cheeseburgers and 3 medium fries for $16.53. The Greens bought 5 cheeseburgers and 4 medium fries for $21.11. Using \( c \) for the cost of a cheeseburger and \( f \) for the cost of medium fries: Write a system of equations that models this situation.
Two families went to a fast-food restaurant in a state with no sales tax. The Browns bought 4 cheeseburgers and 3 medium fries for $16.53. The Greens bought 5 cheeseburgers and 4 medium fries for $21.11. Using \( c \) for the cost of a cheeseburger and \( f \) for the cost of medium fries: Write a system of equations that models this situation.
1
The Greens claimed that each cheeseburger cost $2.49 and each order of medium fries cost $2.87. Are they correct? Justify your answer.
The Greens claimed that each cheeseburger cost $2.49 and each order of medium fries cost $2.87. Are they correct? Justify your answer.
1
Determine algebraically the cost of one cheeseburger and one order of medium fries.
Determine algebraically the cost of one cheeseburger and one order of medium fries.
1
Allysa spent $35 to purchase 12 chickens, buying two different types: Americana and Delaware chickens. Americana chickens cost $3.75 each, and Delaware chickens cost $2.50 each. Write a system of equations to determine the number of Americana chickens \( A \) and Delaware chickens \( D \) she purchased.
Allysa spent $35 to purchase 12 chickens, buying two different types: Americana and Delaware chickens. Americana chickens cost $3.75 each, and Delaware chickens cost $2.50 each. Write a system of equations to determine the number of Americana chickens \( A \) and Delaware chickens \( D \) she purchased.
1
Determine algebraically how many of each type of chicken Allysa purchased.
Determine algebraically how many of each type of chicken Allysa purchased.
1
Each Americana chicken lays 2 eggs per day, and each Delaware chicken lays 1 egg per day. Allysa sells eggs by the dozen for $2.50. Determine the expected revenue at the end of the first week with her 12 chickens.
Each Americana chicken lays 2 eggs per day, and each Delaware chicken lays 1 egg per day. Allysa sells eggs by the dozen for $2.50. Determine the expected revenue at the end of the first week with her 12 chickens.
1
At a local garden shop, the cost of plants includes sales tax. The cost of 4 large plants and 8 medium plants is $40. The cost of 5 large plants and 2 medium plants is $28. If \( l \) is the cost of a large plant and \( m \) is the cost of a medium plant: Write a system of equations to model this situation.
At a local garden shop, the cost of plants includes sales tax. The cost of 4 large plants and 8 medium plants is $40. The cost of 5 large plants and 2 medium plants is $28. If \( l \) is the cost of a large plant and \( m \) is the cost of a medium plant: Write a system of equations to model this situation.
1
Could one large plant cost $5.50 and one medium plant $2.25? Justify your answer.
Could one large plant cost $5.50 and one medium plant $2.25? Justify your answer.
1
Determine algebraically the cost of a large plant and a medium plant.
Determine algebraically the cost of a large plant and a medium plant.
1
In function notation, write A(x) to represent the total cost of attending carnival A and going on x rides.
In function notation, write A(x) to represent the total cost of attending carnival A and going on x rides.
1
In function notation, write B(x) to represent the total cost of attending carnival B and going on x rides.
In function notation, write B(x) to represent the total cost of attending carnival B and going on x rides.
1
Determine the number of rides Marnie can go on such that the total cost of attending each carnival is the same.
Determine the number of rides Marnie can go on such that the total cost of attending each carnival is the same.
1
Marnie wants to go on five rides. Determine which carnival would have the lower total cost. Justify your answer.
Marnie wants to go on five rides. Determine which carnival would have the lower total cost. Justify your answer.
1
Write a system of equations representing how much each company charges.
Write a system of equations representing how much each company charges.
1
Determine and state the number of hours that must be worked for the cost of each company to be the same.
Determine and state the number of hours that must be worked for the cost of each company to be the same.
1
If it is estimated to take at least 35 hours to complete the job, which company will be less expensive? Justify your answer.
If it is estimated to take at least 35 hours to complete the job, which company will be less expensive? Justify your answer.
1
Franco and Caryl went to a bakery to buy desserts. Franco bought 3 packages of cupcakes and 2 packages of brownies for $19. Caryl bought 2 packages of cupcakes and 4 packages of brownies for $24. Let x equal the price of one package of cupcakes and y equal the price of one package of brownies. Write a system of equations that describes the given situation.
Franco and Caryl went to a bakery to buy desserts. Franco bought 3 packages of cupcakes and 2 packages of brownies for $19. Caryl bought 2 packages of cupcakes and 4 packages of brownies for $24. Let x equal the price of one package of cupcakes and y equal the price of one package of brownies. Write a system of equations that describes the given situation.
1
Graph the system of equations on the set of axes provided.
Graph the system of equations on the set of axes provided.
1
Determine the exact cost of one package of cupcakes and the exact cost of one package of brownies in dollars and cents. Justify your solution.
Determine the exact cost of one package of cupcakes and the exact cost of one package of brownies in dollars and cents. Justify your solution.
1
Central High School had five members on their swim team in 2010. Over the next several years, the team increased by an average of 10 members per year. The same school had 35 members in their chorus in 2010. The chorus saw an increase of 5 members per year. Write a system of equations to model this situation, where x represents the number of years since 2010.
Central High School had five members on their swim team in 2010. Over the next several years, the team increased by an average of 10 members per year. The same school had 35 members in their chorus in 2010. The chorus saw an increase of 5 members per year. Write a system of equations to model this situation, where x represents the number of years since 2010.
1
Graph this system of equations on the set of axes provided.
Graph this system of equations on the set of axes provided.
1
Explain in detail what each coordinate of the point of intersection of these equations means in the context of this problem.
Explain in detail what each coordinate of the point of intersection of these equations means in the context of this problem.