<p>I just finished Section 2 of Blue Book practice test #2 and came across a problem that I can not seem to wrap my head around. It is number 19.</p>
<p>The square of x is equal to 4 times the square of y. If x is 1 more than twice y, what is the value of x?
(A) -4
(B) -(1/2)
(C) (-1/4)
(D) 1/4
(E) 1/2</p>
<p>The answer is choice (E) 1/2.
Even after reading the answer explanations on college board's website, I still do not quite understand the problem. Could anyone explain it to me?</p>
<p>I can get to X^2 = 4y^2 and X = 2y +1 but then I'm not sure what to do to find x. I've been doing so many math questions I think I'm a little burnt out on them right now.</p>
<p>Another tip: start with plugging in “x=2y+1” instead of solving for x in the first equation because you will get two possible values for x (plus or minus), which leads to more work and greater chance of error.</p>
<p>I don’t quite agree with the approach above.</p>
<p>You need to deal with the 2 possible solutions for x, and (for this question) eliminate 1. My sense is that there can be questions where you’ll need to process both possible solutions.</p>
<p>x² = 4y² means that x is either 2y or -2y. Start here.</p>
<p>First for the x = 2y case (plugging in the second equation) you get 2y = 2y + 1. That’s not possible, so eliminate this case.</p>
<p>Then for the x = -2y case you get -2y = 2y + 1 and so y = - 1/4 and x = 1/2.</p>
<p>@fogcity. The approach you’re mentioning does lead to multiple solutions that need to be checked. BUT the solution above is correct as is - the square root property is never used.</p>