The system of equations 2x + 4y = 6 and 4x + 8y = 6 has

Given equations 2x + 4y = 6 and 4x + 8y = 6
then,
a₁/a₂ = 2/4 = 1/2;
b₁/b₂ = 4/8 = 1/2;
c₁/c₂ = 6/6 = 1
∴ a₁/b₂ = b₁/b₂ ≠ c₁/c₂
So there is no solution for these equations.