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Math Help - System of equations using mod

  1. #1
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    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?
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  2. #2
    Junior Member ignite's Avatar
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    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)
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