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SAT Math 1.3 Numbers and Operations. x and y must be which of the following?
SAT Math 3.4 Algebra and Functions 239 Views
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Description:
SAT Math 3.4 Algebra and Functions
Transcript
- 00:02
Put this in your calculator and shmoop it...
- 00:05
2 xy + 2 = 1 over x + y.
- 00:09
Solve for y in terms of x.
- 00:11
And here are the potential answers...
- 00:18
It's important to remember that when a question asks us to solve for something in terms of
Full Transcript
- 00:21
something else, it's just asking us to isolate the variable.
- 00:27
So let's get started. We need to isolate y.
- 00:30
We can do this by putting all the terms with y's on one side first.
- 00:34
We subtract y from both sides, and 2 from both sides.
- 00:38
Next, we'll factor out the y on the left side of the equation, and we're left with y times
- 00:42
the quantity 2x - 1 is equal to 1/x - 2.
- 00:47
Then, we divide both sides by 2x - 1, so our y is isolated.
- 00:52
We can factor out 1/x from the top half of the right side,
- 00:56
and we'll be left with (1/x)(1 - 2x) on top.
- 01:02
Now, the top has 1 - 2x, and the bottom has 2x - 1.
- 01:06
Well look at them closely...they're just negatives of each other.
- 01:09
So, we can rewrite the bottom as -1 times 1 - 2x
- 01:15
We can clearly see that 1 - 2x can be cancelled out.
- 01:18
We're left with y = -1/x.
- 01:23
So our answer is (A).
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