Find the smallest positive integer that has remainder 2 when divided by 5, remainder 3 when divided by 7, remainder 4 when divided by 9, and remainder 5 when divided by 11. Hint: Solve 2+5k=3(mod 7) to start, and continue.

Solving 2+5k=3(mod 7) I think gives that 7 divides 5k-1, and so, 7 divides 5k+6, but I don't know how that helps or where to go from here.