Hello I have the following question. ---- Solve the following congruences simultaneously: [tex]2x + 3y \equiv 2 mod 631[/tex] [tex]3x + 2y \equiv 3 mod 631[/tex] ---- I first tried adding and got [tex]5x + 5y \equiv 5 mod 631[/tex], but I was then stuck, so I tried the old multiplication, which looked worse as: [tex]6x^2 + 13xy + 6y^2 \equiv 6 mod 631[/tex] Any ideas? I am guessing that I need to go somewhere with the addition one, but I can't see where. The instructor had a hint of using the fact that 631 is prime, but I can't see anything from that. Thanks. Hmm, just got an idea, [tex]5(x + y) \equiv 5 mod 631[/tex], then find inverse of 5 and multiply it through to find x+y = something mod 631. I did this and got: [tex]x + y \equiv 5*79380 mod 631[/tex] which is [tex]x + y \equiv 1 mod 631[/tex] Now where can I go from here? Any ideas?