algebra I
posted by Brittani .
System of Equations
I need help with the following problem:
A youth group with 26 members is going skiing. Each of the five chaperones will drive a van or a sedan. The vans can seat 7 people and the sedans can seat five people. How many of each type of vehicle could transport all 31 people to the ski area in one trip?
I used the following equation:
7x + 5y = 31. (x= van, y=sedan)
7x=315y.
I divdied by 7 on both sides.
x=315y/7.
This is where I got stuck. What am I doing wrong?

You have only one equation. You need another.
x + y = 5 (vans + sedans = 5)
Next, you make an error in your last statement.
7x=315y so
x = (315y)/7
However, I would do it an easier way unless your teacher told you to solve by substitution. I would solve by elimination.
x+y=5
7x+5y=31
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Multiply top equation by 7
7x+7y=35
7x+5y=31
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Now subtract equation 2 from equation 1 to obtain
2y=4 with y = 2, then solve for x.