Show that the line of intersection of the planes \[x+2y-z=2\]and\[3x+2y+2z=7\] is parallel to the line \[\langle x,y,x\rangle =\langle 1+6t,3-5t,2-4t\rangle\] Find the equation of the plane determined by these two lines.

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I can do the first part, the trouble I am having is finding the plane. How can I do this?

first, solve the system
\[ \large \begin{cases}
x+2y-z=2\\ 3x+2y+2z=7
\end{cases} \]

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