# Homework Help: Solutions to a Linear System

1. Aug 29, 2015

### yango_17

1. The problem statement, all variables and given/known data
Find all solutions of the linear system
x + 2y + 3z = a
x + 3y + 8z = b
x + 2y + 2z = c
where a,b, and c are arbitrary constants.
2. Relevant equations

3. The attempt at a solution
Using elimination, I managed to set the coefficients on the diagonal equal to 1, which then allowed me to solve for z, which was z = -c + a. Substituting z into the other equations to obtain x and y, I ended up with the following solution:
x= -6a - 2b + 13c
y = b + 4a -5c
z = a - c
I was wondering if my method of solving is valid, and if the answer I obtained seems reasonable. Thanks.

2. Aug 29, 2015

### Student100

Your z looks correct, but I get something different for y and x. Recheck your work, and I'll recheck mine.

3. Aug 29, 2015

### yango_17

I plugged my values back into the original system and the equalities don't match up. Now I'm just trying to find out where my mistake was.

4. Aug 29, 2015

### Student100

I just redid it, your Z is correct, so start back from there. I'm assuming you just made a calculation error with y. Your a is positive (and smaller than it should be), while it should be negative. Same deal with your C.