### 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: .