But equation (1) states $3v_2 + v_3 = -4$. This inconsistency implies no solution exists unless $\mathbf{d}$ is orthogonal to $\mathbf{c}$. Check $\mathbf{d} \cdot \mathbf{c} = (-4)(2) + (5)(-1) + (1)(3) = -8 -5 +3 = -10