Find the equation of the plane passing through the intersection of and and passing through

I forgot how these sums are done:Here's what I did:

solving the two equations we get and

hence we get the parametric equation:

hence the direction vectors=

as the line is perpendicular to the intersection, it is also the normal vector of the 3rd plane:

equation of required plane:

putting we get

new simplified equation:

but the answer given in the book is:

What am I doing wrong here?

thanks in advance.