Interpret Solutions to Systems

Erin is 3 years younger than twice Alex's age. Their ages combined are 33 years. How old are Alex and Erin. If x=Erin's age and y=Alex's age, choose the system that matches the situation.

• x + y = 33
  y = 2x - 3

• x + y = 33
  x = 2y - 3

• x + y = 33
  x = 3 - 2y

• x + y = 3
  x = 33 - 2y

Nancy went to the grocery story. On Monday she purchased 4 apples and 6 bananas for a total of $13. On Wednesday she purchased 3 apples and 7 bananas for a total of $13.50. Define the variables in the system:

4x + 6y = 13

3x + 7y = 13.5

• x = number of apples

  y = number of bananas

• x = number of bananas

  y = number of apples

• x = price of one apple

  y = price of one banana

• x = price of one banana

  y = price of one apple

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

Some students want to order shirts with their school logo. One company charges $9.65 per shirt plus a setup fee of $43. Another company charges $8.40 per shirt plus a $58 fee. Define the variables in the system:

y = 9.65x + 43

y = 8.40x + 58

• x = price of one shirt

  y = price of order

• x = price of order

  y = price of one shirt

If a system of linear equations has one solution, what does this mean about the two lines? 

• Parallel lines

• Identical lines 

• Intersecting lines

• A

• B

• C

• D

If a system of linear equations has one solution, what does this mean about the two lines?

• Parallel lines

• the same line

• Intersecting lines

Select the statement that correctly interprets Peter's solution.

• x = 0

• There is No Solution because -5=-5 is a true statement.

• There are Infinite Solutions because -5=-5 is a true statement.

• The solution is the ordered pair (-5, -5)

Homer sells tickets for admission to your school play and collects a total of $104. Admission prices are $6 for adults and $4 for children. He sold 21 tickets total. Solve the system:

x + y = 21

6x + 4y = 104

• 10 adult tickets, 11 child tickets

• 11 adult tickets, 10 child tickets

Ryley sold 10 packages of sugar cookies and 2 packages of oatmeal cookies for $56. Luke sold 9 packages of sugar cookies and 3 packages of oatmeal cookies for $60. What is the price of 1 pack of sugar cookies and 1 pack of oatmeal cookies?

• Sugar Cookies $8

  Oatmeal Cookies $4

• Sugar Cookies $4

  Oatmeal Cookies $8

• Sugar Cookies $2

  Oatmeal Cookies $6

• Sugar Cookies $6

  Oatmeal Cookies $2