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
I feel like a big dummy because every time I try to rework this problem, I come to the same wrong answer. I know that I have to be leaving something out.
A) -4
B) -1/2
C) -1/4
D) 1/4
E) 1/2
I feel like a big dummy because every time I try to rework this problem, I come to the same wrong answer. I know that I have to be leaving something out.
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I think choice (E) is right:
First, try to write equations based on the wording of the question. The two equations I get from that are x^2=4y^2 and x=2y+1. Now, just plug in x in terms of y into the first equation to get
(2y +1)^2 = 4y^2
4y^2 + 4y + 1 = 4y^2
4y + 1 = 0
y = -1/4
Then, plug y=-1/4 into x=2y + 1 to get x=1/2.
Basically, it's just a standard system of equations problems. I think the trickiest part of the problem is translating the wording into correct equations; just take some time to think about what the words are saying. They love to test that skill on the SAT, so it's a good idea to get confident with it.
Also, just for your additional knowledge, the x^2=4y^2 equation is a bit tricky, because it actually describes two separate lines. You could have tried to solve this equation for x and plugged it into the other one, but you have to be very careful to remember that whenever you take a square root to cancel a squared variable, you have to set it equal to the positive and negative of the square root of the other side. You can try this for yourself and see that one of the equations will yield the answer that we got, and the other will yield no solution, implying that one of the two lines described by x^2=4y^2 does not intersect with x=2y+1.
First, try to write equations based on the wording of the question. The two equations I get from that are x^2=4y^2 and x=2y+1. Now, just plug in x in terms of y into the first equation to get
(2y +1)^2 = 4y^2
4y^2 + 4y + 1 = 4y^2
4y + 1 = 0
y = -1/4
Then, plug y=-1/4 into x=2y + 1 to get x=1/2.
Basically, it's just a standard system of equations problems. I think the trickiest part of the problem is translating the wording into correct equations; just take some time to think about what the words are saying. They love to test that skill on the SAT, so it's a good idea to get confident with it.
Also, just for your additional knowledge, the x^2=4y^2 equation is a bit tricky, because it actually describes two separate lines. You could have tried to solve this equation for x and plugged it into the other one, but you have to be very careful to remember that whenever you take a square root to cancel a squared variable, you have to set it equal to the positive and negative of the square root of the other side. You can try this for yourself and see that one of the equations will yield the answer that we got, and the other will yield no solution, implying that one of the two lines described by x^2=4y^2 does not intersect with x=2y+1.