Back again with another difficult SAT math problem. This one involves some tough algebra that many students might trip up on. If you're an algebra ace, this problem won't take too much of your time. If you're not, then luckily we have tricks to solve multiple choice questions without doing the algebra at all. In fact, all we'll need to know is PEMDAS. Using the trick, in this case, wont even waste much time.
If x=5+4t^2 and y=3+2t, what is x in terms of y?
a) y^2-6y+14
b) y^2+6y+14
c) 4y^2-24y+36
d) 4y^2-24y+41
e) 4y^2+24y+41
Yet again, I'll start out using tricks that involve less advanced algebra. Pick a number for 't'. I usually stay away from 0 or 1 when doing this, as multiplying by 1 or 0 can make multiple answers look possible. I'm going with 2. So x=5+4(2)^2-->x=21. And y=3+2(2)-->y=7. Now we just need to plug y=7 into the answer choices and see which one gives us
21.
a)7^2-6(7)+14-->49-42+14=21.... there's our answer already.
b)7^2+6(7)+14-->49+42+14=63
c)4*7^2-24*7+36 -->196-168+36=64
d)4*7^2-24*7+41 -->196-168+41=69
e)4*7^2+24*7+41 -->196+168+41=405
*notice that by choosing 2 for t gave us different numbers for every answer choice. This makes it easy to see the right answer right away.
And if you prefer an algebraic approach to the question, you could solve t in terms of y, and substitute into the equation for x:
y=3+2t-->(y-3)/2=t
Now substitute this value of t into the x equation:
x=5+4t^2--> x=5+4[((y-3)/2)^2] *be very careful in squaring the y-3 here, FOIL* x=5+4(y^2-6y+9)/4 --> x=5+y^2-6y+9 --> x=y^2-6y+14 ...
This is answer a.
Always keep in mind that there is (almost) always more than one way to solve a math problem. On multiple choice questions, working backwards can sometimes be easier and faster than going forwards. Testing your answer choices to match the original question is a great tactic for any question you might get stuck on!
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