Test 1 Section 3 - #7 (page 398)

Whenever the SAT asks you to solve for an expression (or, anything but a standard single variable), what you want to ask yourself is: "How do I get from what they gave me to what they want?"  Usually once you see the path, it's only a step or two.

The first thing I want to do here is take what they gave me and break it up so it's more useful.
3x² = 4y = 12 can be broken into two equations:

3x² = 12
 4y = 12 *

Note that we have parts of what we want in both equations (our x² is in the first equation, our y is in the second).  Since we're looking for x²y eventually (those two parts multiplied together), let's multiply our entire equations by each other:

(3x²)(4y) = (12)(12)

12x²y = 144

And now we're almost there!  We want to know what x²y is by itself, so just divide both sides by 12:

x²y = 12

That's choice (D).

* Note that from here we COULD just solve: x = 2 (or -2) and y = 3.  HOWEVER, it's better practice to continue to solve directly for the expression x²y because we're not always going to be able to solve for the component parts on questions like this...at least not quickly.