Two groups of students bought airline tickets to go to a conference. One group bought...

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.

Answer is given below (on video)