# Math Help - solving for 3 unknowns

1. ## solving for 3 unknowns

c + ba = 30
a + bc = 18

SOLVE FOR a, b, c

2. $a,b,c$ are integers?

3. Originally Posted by red_dog
$a,b,c$ are integers?
I guess so..

4. Adding and substracting the two equations we have
$\displaystyle \left\{\begin{array}{ll}(a-c)(b-1)=12\\(a+c)(b+1)=48\end{array}\right.$
So, $b-1$ must divide 12 and $b+1$ must divide 48.
For example:
$b-1=1\Rightarrow b=2\Rightarrow b+1=3|48$.
Replacing $b=2$ in system we have
$\displaystyle \left\{\begin{array}{ll}a-c=12\\a=c=16\end{array}\right.\Rightarrow a=14,c=2$.
And so on...