Show that the curve with vector equation

is the curve of intersection of the surfaces and .

Attempt:

(1)

(2)

plug (1) into (2) for y

Expanding and canceling

(3)

vector equation

(4)

plug (4) into (3)

divide out the 4

identity

therefore 1= 1

Did i even do this correct?

If not where did i go wrong?

Thank you