# Two groups of students bought airline tickets to go to a conference. One group bought two tickets from Airline 1 and three tickets from Airline 2 and their total was $900 before taxes and fees. The other group bought one ticket from Airline 1 and four tickets from Airline 2, and their total was$950 before taxes and fees. How much does a ticket cost of each airline?

Question
Linear equations and graphs
Two groups of students bought airline tickets to go to a conference. One group bought two tickets from Airline 1 and three tickets from Airline 2 and their total was $900 before taxes and fees. The other group bought one ticket from Airline 1 and four tickets from Airline 2, and their total was$950 before taxes and fees. How much does a ticket cost of each airline?

2021-01-11
Let x be the cost of a ticket on Airline 1 and y be the cost of a ticket on Airline 2.
Two tickets from Airline 1 and three tickets from Airline 2 cost $900: 2x+3y=900(1) One ticket from Airline 1 and four tickets from Airline 2 cost$950:
x+4y=950(2)
Solve by substitution. Solve for xx using (2) to obtain (3):
x=950−4y(3)
Substitute (3) to (1) and solve for yy:
2(950−4y)+3y=900
1900−8y+3y=900
−5y=−1000
y=200
Solve for x using (3):
x=950−4(200)
x=950−800
x=150
The cost of a ticket on Airline 1 is $150, and the cost of a ticket on Airline 2 is$200.

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