###### Answer: C

###### Difficulty: Medium

### Strategy #1: Using the **PIA (Plug In Answers)** strategy:

- (A) Is not the right answer because when you plug in -80 for (which doesn’t actually make any sense since can’t equal a negative number), you get . After adding 80 to both sides, you have . So . If you plug that back into the second equation, you get which gives you . If , as we originally presumed, x would not exist in the real number system. Even if you mistakenly thought you could take the square root of a negative number, you might get when you tried to take the square root of both sides, which is not equal to .
- (B) is not the right answer because when you plug in for in the first equation, you get , which gives you . So after you take the square root of both sides, . Looking at the second equation, if , then after you take the square root of both sides you get . Plugging in for x in the second equation gives you y=. This does not match the value we got from the first equation.
- (C) is the correct answer!!! When you plug in for in the first equation, you end up with . After subtracting from both sides, you are left with . After taking the square root of both sides, . Looking at the second equation, if then . So we get which means . This is the same thing we got when we plugged into the first equation! Now we know (C) is the answer!
- (D) is not the right answer because when you plug in for in the first equation, you get , which gives you . So after you take the square root of both sides, . Looking at the second equation, if , then after you take the square root of both sides you get . Plugging in for x in the second equation gives you y=. This does not match the value we got from the first equation

### Strategy #2: Using the **substitution method **

You need to find a solution that works for both equations. Since the y is isolated in the second equation you can substitute into in the first equation.

- (A) is not the right answer. You might have gotten this answer if you forgot to square the when you substituted in for . If this was your mistake, you may have gotten . Upon combining like terms, you may have ended up with . After dividing by you would get .
- (B) is not the right answer. You might have gotten this answer if you solved for , instead of .
- (D) is not the right answer. You might have gotten this answer if you solved for , instead of .
- (C) IS the correct answer!! If you substituted correctly by plugging in for like this: and then correctly simplified the left-hand side like this: leading to , you could then divide both sides by , leaving you with the answer: .