How to solve congruence using diophantine equation?

Question

Id like to know how to solve this congruence, 2x + 5y ≡ 0(mod 7)so far i've tried solving it like a Diophantine equation which gave me 2x + 5y - 7z = 0 and x = (-5/2)y + (7/2)z and got stuck on this step.

Answer 1

Easy to solve in $$2x+5y=7z$$ as, $$x=y=z$$ is a solution trivially. Adding 5 to x, and subtracting 2 from y, also adds 0. Adding or subtracting 0 is idempotent. Adding or subtracting any solutions ( for x and y at least) gives a new solution, for this same reason (we are adding or subtracting 0 mod 7).We Also have adding 6 to x and subtracting 1 from y adds 7.etc So, out to absolute value 10 we have:

• 21 with $x=y=z$
• 14 with $x-5=y+2=z$
• 14 with $x+5=y-2=z$
• etc. (0,0,0) being one of the most trivial 21