Eliminate an expression with Mod operation

Question

The target below should equal 0, since 2x + c = a + b + c = 6c, and Mod[6c,3] == 0

But Mathematica seems to be unable to simplify this expression containing Mod?

It says "target-1/4\ Mod[c+2\ x,3] is not a well-formed equation."

Eliminate[{a == b + c, b == 2 c, a == x + y, b == x - y, 
  target - 1/4 Mod[2 x + c, 3]}, {x, a, b, y}]

Answer 1

Try

Eliminate[{a == b + c, b == 2 c, a == x + y, b == x - y, 
  target == 1/4 (2 x + c), Modulus == 3}, {x, a, b, y}]

which returns Modulus == 3 && target == 0.