solving for 3 unknowns

**hossein** · July 9th 2007, 10:08 AM

c + ba = 30
a + bc = 18

SOLVE FOR a, b, c

**red_dog** · July 9th 2007, 10:25 AM

$a,b,c$ are integers?

**hossein** · July 9th 2007, 10:30 AM

Originally Posted by red_dog

$a,b,c$ are integers?

I guess so..

**red_dog** · July 9th 2007, 10:39 AM

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...

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