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:
.