System of Equations

Emma and Aiden are shopping for candles! Emma paid $64 for 3 large candles and 4 small candles. Aiden, on the other hand, paid $4 more than Emma for 1 large candle and 8 small candles. The price of each large candle is the same, and the price of each small candle is the same. Which system of equations can be used to find the price in dollars of each large candle, x, and each small candle, y?

• A) 4y = 3x + 64 and 8y = x + 68

• B) 4y = 3x + 64 and 8y = x + 60

• C) 3x + 4y = 64 and x + 8y = 68

• D) 3x + 4y = 64 and x + 8y = 60

Zoey and Aarav are working on a system of equations and have graphed them on the grid. Can you help them solve it?

• 
• 
• 
• 

A sports magazine prints 12 issues per year, and a technology magazine prints 10 issues per year. The total number of pages in all the issues of the sports magazine for one year is 32 more than the total number of pages in all the issues of the technology magazine for one year. Each issue of the sports magazine has 18 fewer pages than each issue of the technology magazine. Which system of equations can be used to find ( s ), the number of pages in each issue of the sports magazine, and ( t ), the number of pages in each issue of the technology magazine?

• A. ( s = t - 18 ) and ( 12s = 10t + 32 )

• B. ( t = s - 18 ) and ( 10t = 12s + 32 )

• C. ( s = t - 18 ) and ( 10s = 12t + 32 )

• D. ( t = s - 18 ) and ( 12t = 10s + 32 )

Anaya and Addison are solving a mystery graph puzzle. Can you help them figure out which system of equations is best represented by the graph?

• 3x - y = 2 and 4x + 9y = 36

• 3x - y = 6 and 4x + 9y = 4

• x - 3y = -18 and 9x + 4y = 9

• x + y = 10 and 9x + 4y = 13

Lucas and Priya are organizing a kitchen cabinet with 15 plates. Some plates have a diameter of 7 inches, while others have a diameter of 12 inches. The total diameter of all the plates combined is 140 inches. Can you help them figure out the number of 7-inch plates, x, and the number of 12-inch plates, y, by choosing the correct system of equations?

• A) x + y = 140 and 12x + 7y = 15

• B) 7x + 12y = 140 and 7x + 12y = 15

• C) x + y = 15 and 7x + 12y = 140

• D) x + y = 15 and 12x + 7y = 140

Addison and Rohan are solving a mystery involving a system of linear equations represented by line h and line j. Addison has a table with some points on line h, while Rohan has the graph of line j. Can you help them figure out which system of equations is best represented by lines h and j?

• 
• 
• 
• 

An artist bought a set of 10 paintbrushes that contained x small paintbrushes and y large paintbrushes. The number of small paintbrushes in the set was 4 times the number of large paintbrushes in the set.

Which system of equations can be used to find the numbers of small paintbrushes and large paintbrushes in the set?

• x + y = 10 and x = 4y

• x - y = 10 and x = 4y

• x + y = 10 and y = 4x

• x - y =10 and y = 4x

Thomas and Amelia are working on a system of equations and have graphed it on the grid. Can you help them solve it?

• 
• 
• 
• 

A bag contains 18 coins consisting of quarters and dimes. The total value of the coins is $2.85. Which system of equations can be used to determine the number of quarters, 9, and the number of dimes, d, in the bag?

• 0.10q + 0.25d = 2.85

  q + d = 18

• 0.10q + 0.25d = 18

  q + d = 2.85

• 0.25q + 0.10d = 2.85

  q + d = 18

• 0.25q + 0.10d = 18

  q + d = 2.85

The tables of ordered pairs represent some points on the graphs of two lines.

Which system of equations is represented by the two lines?

• y = 5x -7

  4x -y =4

• y=5x-7

  4x+y=12

• y = 7x - 9

  4x - y = 4

• y = 7x - 9

  4x + y = 12

• None of the Above