# Solving simultaneous equations with 3 parts

I keep trying to solve this problem, but i keep on getting crazy answers, i think i am right up to a certain point and then doing something wrong, the question is to solvie this :

\begin{align*} 2x^2 + 3y + z &= 8\\ x - 2y &= 4\\ 3z - x &= 7 \end{align*}

I've tried many things but can't work out what i'm doing wrong, any help will be appreciated.

You can use $x-2y=4$ to get $\frac{1}{2}x-2=y$. You can use $3z-x=7$ to get $z=\frac{7}{3}+\frac{1}{3}x$. Plug these into $2x^2+3y+z=8$ to get
$$2x^2+3\left(\frac{1}{2}x-2\right) +\frac{7}{3}+\frac{1}{3}x=8.$$
Simplify and use quadratic formula to find values of $x$. Then use the above equations to get $z$ and $y$.