# Solving Linear Systems - Word Problem

• Apr 26th 2011, 09:05 AM
GhitaBelghiti
Solving Linear Systems - Word Problem
A group of 51 people attend a ball game. There were twice as many children as adults in the group. Write a system of equations that you could use to solve this problem, where (a) is the number of adults and (c) is the number of children in the group.
Solve the system of equations for (c), the number of children in the group.
• Apr 26th 2011, 09:10 AM
SpringFan25
the first equation is:
a + c = 51

the question says that the number of adults is 2 * number of children. Can you write the second equation from that?
• Apr 26th 2011, 09:16 AM
GhitaBelghiti
I've tried equations like: 51= c+2a and c=51-2a but they don't seem to work.
• Apr 26th 2011, 09:19 AM
SpringFan25
if
c = number of children

Then you are told that:
"number of adults + number of children = 51" : a + c = 51
"number of children is twice number of adults": c = 2a

Note: i copied the question wrong in my previous post. there are twice as many children, not twice as many adults.
• Apr 26th 2011, 09:24 AM
GhitaBelghiti
Thank You!!
• Apr 26th 2011, 09:29 AM
GhitaBelghiti
Solving Linear Systems by Elimination
5x+6y=23
4x-6y=-14

I've tried it:
5x+6y=23
-
4x-6y= -14
_______________

x = 37

Then I did this:

5(37)+6y=23

185+6y=23
-185 -185

6y=-162
--- ----
6 6

y = -27

But when I plug those numbers in, it doesn't work. Help please :)
• Apr 26th 2011, 09:39 AM
SpringFan25
this doesn't seem to be related to the question you posted at the top.

you forgot that 6y - (-6y) = 12y. so it would be:

5x+6y=23
-
4x-6y= -14
----------------
x + 12y = 37