Algebra 5.3-5.4 Quiz

Solve using elimination.

x - 7y = 25

x + 12y = 6

Solve using elimination. You may have to rearrange your equation first.

9x - 4y = -55

3x = -4y - 21

Solve using elimination.

2x - y = 8

3x + y = 17

Solve using elimination.

x + 3y = 1

-5x + 4y = -24

Solve using elminiation.

3x - 5y = -16

2x - 3y = -8

Solve using elimination. You may have to rearrange the equations first.

-2x - 9y = -23

4x - 19 = -9y

Two families go skiing on a Saturday. One family purchases two adult lift tickets and four youth lift tickets for $166. Another family purchases four adult lift tickets and five youth lift tickets for $263. Let x represent the cost in dollars of one adult lift ticket and let y represent the cost in dollars of one youth lift ticket. Solve the linear system to find the cost of one adult and one youth lift ticket.

Bonus

Greyson has a paper delivery route which he completes by riding his bicycle. The drop-off station where he picks up his papers for delivery is located in the neighborhood where he delivers papers. When riding between his house and the drop-off station, Greyson averages 10 miles per hour. On Monday through Saturday the paper is a small daily and Greyson averages ½ mile per hour while making his deliveries. When delivering the small daily it takes Greyson 4 hours and 18 minutes, from the moment he leaves his house to the moment he returns in order to complete his route. On Sundays, the paper is much larger and he averages 1/3 mile per hour while making his deliveries, which adds an additional 2 hours to the time it takes to complete his route.

a. Write a linear system to model this situation, where x represents the miles from Greyson’s house to the drop-off station and y represents the length of the route (in miles).

b. What is the distance from Greyson’s house to the drop-off station?

c. What is the length of the paper route?