Systems Applications (Desmos)

Solve the System:

2x + 5y = 55

y = 2x – 1

• (5, 9)

• (4, 10)

• (5, 11)

• (12, 9)

Solve the System:

3X + 5Y = 20

2X + 4Y = 14

• (5, 1)

• (1, 5)

• (5, 4)

• (1, 7)

What is Y in the solution of the following system of equations?

Y = 2X

2X + 3Y = 48

• 3

• 6

• 12

• 24

What is the value of X+Y in the following system of equations?

5X + 3Y = 16

2X – 3Y = 19

• –3

• 2

• 5

• 8

What is the value of X – Y given the following system of equations?

2X – 3Y = 33

Y = –X – 1

• 6

• –7

• –1

• 13

John and his children went into a movie theater and he bought $44.25 worth of drinks and pretzels. Each drink costs $5 and each pretzel costs $4.75. He bought twice as many drinks as pretzels.

Which system of equations could be used to determine the number of drinks, D, and the number of pretzels, P, that John purchased?

• 5D + 4.75P = 44.25

  D = 2P

• 4.75D + 5P = 44.25

  D = 2P

• 5D + 4.75P = 44.25

  P = 2D

• 4.75D + 5P = 44.25

  P = 2D

John and his children went into a movie theater and he bought $44.25 worth of drinks and pretzels. Each drink costs $5 and each pretzel costs $4.75. He bought twice as many drinks as pretzels. Determine the number of drinks and the number of pretzels that John bought.

• 6 Drinks

  3 Pretzels

• 3 Drinks

  6 Pretzels

• 4 Drinks

  8 Pretzels

• 8 Drinks

  4 Pretzels

Joshua is a songwriter. He collects royalties on his songs whenever they are used in media. He earns $30 for every commercial and $120 for every movie that features one of his songs. Last year, Joshua earned $420 in royalties. His songs were featured in 4 more commercials than movies.

Which system of equations could be used to determine the number of times Joshua's songs were featured in a commercial, C, or a movie, M?

• 30C + 120M = 420

  C = M + 4

• 120C + 30M = 420

  C = M + 4

• 30C + 120M = 420

  M = C + 4

• 120C + 30M = 420

  M = C + 4

Joshua is a songwriter. He collects royalties on his songs whenever they are used in media. He earns $30 for every commercial and $120 for every movie that features one of his songs. Last year, Joshua earned $420 in royalties. His songs were featured in 4 more commercials than movies. Determine how many commercials and how many movies featured Joshua's song?

• 6 Commercials

  2 Movies

• 2 Commercials

  6 Movies

• 10 Commercials

  6 Movies

• 6 Commercials

  10 Movies

Andres is a high school basketball player. In a particular game, he made some two-point shots and some free throws (worth one point each). Andres made a total of 12 shots altogether and scored a total of 16 points.

Which system of equations could be used to determine the number of two-point shots, T, Andres made and the number of free throws, F, he made?

• T + F = 12

  2T + F = 16

• T + F = 16

  2T + F = 12

• T + F = 16

  T + 2F = 12

• T + F = 12

  T + 2F = 16