Posted by **Brittani** on Thursday, January 15, 2009 at 11:57pm.

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=31-5y.

I divdied by 7 on both sides.

x=31-5y/7.

This is where I got stuck. What am I doing wrong?

- algebra I -
**DrBob222**, Friday, January 16, 2009 at 12:12am
You have only one equation. You need another.

x + y = 5 (vans + sedans = 5)

Next, you make an error in your last statement.

7x=31-5y so

x = (31-5y)/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

===============

Multiply top equation by 7

7x+7y=35

7x+5y=31

===========

Now subtract equation 2 from equation 1 to obtain

2y=4 with y = 2, then solve for x.

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