systems

There are 15 plates in a kitchen cabinet. The diameter of each plate is either 7 inches or 12 inches. The diameter of all 15 plates combined is 140 inches.

Which system of equations of equations can be used to find the number of 7-inch plates, x, and number of 12-inch plates, y, that are in the cabinet?

• x + y = 140

  12x + 7y = 15

• 7x + 12y = 140

  7x + 12y = 15

• x + y = 15

  7x + 12y = 140

• x + y = 15

  12x + 7y = 140

A drummer and a guitarist each wrote songs for their band. The guitarist wrote 8 fewer than twice the number of songs that the drummer wrote. They wrote a total of 46 songs.

Which system of equations models this situation if the drummer wrote d songs and the guitarist wrote g songs?

• g = 2d - 8

  g + d = 46

• g = 8 - 2d

  g = 46 - d

• d = 2g - 8

  d = 46 - g

• d = 8 - 2g

  d + g =46

The graph of 2 lines are shown. Which system is best represented by this graph?

• 3x - y = 2

  4x + 9y = 36

• 3x - y = 6

  4x + 9y = 4

• x - 3y = -18

  9x + 4y = 9

• x + y = 10

  9x + 4y = 13

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 technology magazine for one year. Each issue of the sports magazine has 18 fewer pages than the each issue of the technology magazine. Which system 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?

• s = t - 18

  12s = 10t + 32

• t= s - 18

  10t = 12s +32

• s = t - 18

  10s = 12t + 32

• t= s - 18

  12t = 10s +32

A bag contains 18 coins consisting of quarters and dimes. The total values of the coins is $2.85. Which sytem of equations can be used to determine the number of quarters, q, 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

Which graph represents a system of equations that has no solution?

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Which graph can be used to find the solution to the system of equations below?

2x + y = -4

-3y = 2x +12

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Two customers went to a post office to buy postcards and large envelopes. Each postcard costs the same amount, and each large envelope costs the same amount.

The first customer paid $12 for 14 postcards and 5 large envelopes.

The second customer paid $24.80 for 10 postcards and 15 large envelopes.

What was the cost in dollars of each large envelope?

• $1.42

• $0.35

• $1.15

• $0.63

What is the x-value of the soltion to this system of equations?

x = 2y - 4

7x + 5y = -66

• -2

• $-\frac{19}{7}$

• -8

• $-\frac{62}{19}$

A bus travels two different routes: the Green Route and the Blue Route. The Routes are different lengths.

On Monday the bus traveled the Green Route 6 times and the Blue Route 5 times, traveling a total of 52 miles.

On Tuesday the bus traveled the Green Route 12 times and the Blue Route 13 times, traveling a total of 119 miles.

What is the length of the Green Route in miles?

• 4.4 mi

• 4.5 mi

• 6.4 mi

• 6.8 mi