# System of equations using mod

• April 26th 2012, 09:25 AM
System of equations using mod
If i have two equations ,

11a+b(mod26)=17
&
22a+b(mod26)=22

How do i begin to solve for a and b? Ive been trying to make vectors out of them and i get for a=11/5, but this doesn't sound right, i think i should be getting whole numbers shouldn't i?
• April 26th 2012, 09:34 AM
ignite
Re: System of equations using mod
$22a+b \equiv 22$ (mod 26)
$11a+b \equiv 17$ (mod 26)
$\Rightarrow 11a \equiv 5$(mod 26)
$\Rightarrow a \equiv 5.11^{-1}$(mod 26)
$11^{-1}=19$ Since $11.19 \equiv 1$ (mod 26)
$\Rightarrow a \equiv 5.19$(mod 26)
$\Rightarrow a \equiv 17$ (mod 26)