Writing and solving systems of equations

A bag contains 18 coins consisting of quarters and dimes. The total value of the coins is $2.85. 

Which systems of equations can be used to determine the number of quarters, q, and the number of dimes, d, in the bag?

Solve the system of equations using the substitution method.

• (1, 3)
• (-7, -4)
• Infinitely Many Solutions
• (4.25, -.65)

Alexandra finds that she can give 3 haircuts and 2 hair dyes in 315 minutes. Giving 2 haircuts and 4 hair dyes takes 450 minutes. Let h represent the number of haircuts given and d represent the number of hair dyes done. Which system of equations represents the situation?

• 3h + 2d = 315

  2h + 4d = 450

• 3h + 2d = 450

  2h + 4d = 315

• 2h + 4d = 315

  3h + 2d = 450

• 3h + 2d = 315

  2h + 2d = 135

The talent show committee sold a total of 530 tickets in advance. Student tickets cost $3 each and the adult tickets cost $4 each. If the total receipts were $1740, which system could be used to find how many of each type of ticket were sold?

• S + A = 530
  3S + 4A = 1740
• S + A = 530
  4S + 3A = 1740
• S + A = 1740
  3S + 4A = 530
• S + A = 1740
  4S + 3A = 530

Solve the system of equations using the substitution method.

• (-7, 4)
• Infinitely Many Solutions
• (13, -5)
• (0, -8)

Solve for x and y by using the substitution method.

3x + 2y = 16

y = -7x + 19

• (-2,5)

• (-2,-5)

• (2,-5)

• (2,5)

Solve the system of equations.

• (11, 21)

• (3, 11)

• (11, -67)

• No solution

• Infinite solutions

Caitlin won a bag full of money! She has 49 bills in all. She counts $1,430. There are twenty-dollar bills and fifty-dollar bills. How many of each bill does Caitlin have? Which system best represents the situation?

• x + y = 1430

  20x + 50y = 49

• x + y = 49

  10x + 5y = 1430

• x + y = 49

  20x + 50y = 1430

• x + y = 49

  x + y = 1430

Solve the system using the substitution method.

x + 3y = 9

2x + y = −2

• (3,2)

• (-2, 2)

• (3, -4)

• (-3, 4)

• (0.5, -3)

CHALLENGE: Three equations.
x + y + z = 4
x = -2y
z = -3y
Solve the system of equations using substitution.

• x = 2
  y = -1
  z = 3
• x= -5
  y = 3
  z = 1
• x = 10
  y = -2
  z = 0
• x= 4
  y = 1
  z = -1