multivariable- intersecting planes and curves

[acpodgorski]

so this question tells me to show the curve of intersection of the surfaces x+2y^2-z^2+3x=1 and 2x^2+4y^2-2z^2-5y=0 lies in a plane and i just need help getting started to find the where they intersect(as far as i know) Do i need to find their normal vectors?

 

[tkhunny]

If it were me, first, I'd do some completing of the square and ponder the two surfaces.

Second, I'd solve each for z^2 and ponder on the Transitive Property of Equality.