Plane through a point and the line of intersection of other two planes 
Find the equation of the plane through $(-1,4,2)$ and containing the line of intersection of the planes $$4x-y+z-2=0 \\ 2x+y-2z-3=0$$

My answer comes out to be:
$$-9x-67y+104=51$$
While the answer provided on the answer sheet is:
$$4x-13y+21z=-14$$
Could you please check if the answer calculated by me is correct or the one provided on the answer sheet.

HINT:
$$\begin{cases}
4x-y+z-2=0\\
2x+y-2z-3=0
\end{cases}\Longleftrightarrow$$
$$\begin{cases}
z=-4x+y+2\\
2x+y-2z-3=0
\end{cases}\Longleftrightarrow$$
$$\begin{cases}
z=-4x+y+2\\
2x+y-2(-4x+y+2)-3=0
\end{cases}\Longleftrightarrow$$
$$\begin{cases}
z=-4x+y+2\\
10x-y-7=0
\end{cases}\Longleftrightarrow$$
$$\begin{cases}
z=-4x+y+2\\
y=10x-7
\end{cases}\Longleftrightarrow$$
$$\begin{cases}
z=-4x+(10x-7)+2\\
y=10x-7
\end{cases}\Longleftrightarrow$$
$$\begin{cases}
z=6x-5\\
y=10x-7
\end{cases}$$
