Question

PROVE: if a divides b and a divides c, then a divides bx+cy.

Answer 1

hmm..

Well, if a divides b, that means there is some number N such that a*N = b. And if a divides c, then that means there is some number K such that a*K = c. Then substitute in your equation

a*N(x) + a*K(y)

Both terms can be divided by a and therefore is divisible by a.

a(Nx + Ky)

Answer 2

since a divides b, b=a*n where n is some integer, since a divides c , c=a*m