Using Lagrange multipliers to solve the following system of equations; getting imaginary numbers

Question

Using Lagrange multipliers, solve the system of equations:

1. $2x=\lambda(8x)+2\mu$
2. $2y=\lambda(8y)$
3. $2z=\lambda(-2z)+4\mu$

with constraints:

$4x^2+4y^2-z^2=0$ and $2x+4z=7$

So solving for $\lambda$ in (2), I get $\lambda=\frac{1}4$, and continuing I get $\mu=0, z=0, x=\frac{7}2$ but for $y$ I get an imaginary number. Am I doing something wrong here? I am sure that the equations and constraints are correct.