Page 199 - Math Course 2 (Book 1)

Methods of Solving Systems of Equations

CAR RENTAL You can use elimination to solve.
Ace Car Rental rents a car for $45 a
day and $0.25 per mile. Star Car Rental y = 45 + 0.25x
rents a car for $35 per day and $0.30 per mile. How (–)y = 35 + 0.30x
many miles would a driver need to drive before the 0 = 10 – 0.05x
cost of renting a car at Ace Car Rental and renting a –10 = –0.05x
car at Star Car Rental were the same?
200 = x
Explore
You know the cost to rent a car for each company. This means that after 200 miles,
Answer
the cost will be the same.
Plan
Write an equation to represent the cost for each
company. Then solve. Check
Check by sketching a graph of the equations.
Solve The graphs appear to intersect at (200, 95) which
Let x = the number of miles and y = the cost of verif es that x = 200.
renting a car.
Ace Car Rental: y = 45 + 0.25x
Star Car Rental: y = 35 + 0.30x

Your Turn!

Determine the Best Method

POOL PARTY VIDEO GAMES
At the school pool party, Mr. Lewis bought 1 adult The cost to rent a video game from Action Video
ticket and 2 child tickets for $10. Mrs. Vroom is $2 plus $0.50 per day. The cost to rent a video
bought 2 adult tickets and 3 child tickets for $17. game at TeeVee Rentals is $1 plus $0.75 per day.
All adult tickets are the same price and all child After how many days will the cost of renting a
tickets are the same price. The following system video game at Action Video be the same as the
can be used to represent this situation. Determine cost of renting a video game at TeeVee Rentals?
the best method to solve the system of equations.
Then solve the system. A. 8 days
x + 2y = 10 B. 4 days
2x + 3y = 17 C. 2 days
D. 1 day
A. (4, 3) Answer
B. (4, 4)
C. (3, 3)
D. (–4, –3)

Answer

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