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.

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