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### Please graph and send the solution for:

```
Date: 23 May 1995 16:43:06 -0400
From: J. Poholsky's grade6A Charles River
Subject: math problem

Please graph and send the solution for:

x^2/2  +  y^2/2 = 0

from Katie Allen and Kim Wilson
problem from Mr. Rob Hunt
Charles River School in Dover Ma.
```

```
Date: 24 May 1995 00:37:13 -0400
From: Dr. Sydney
Subject: Re: math problem

Dear Katie and Kim,

Hello! This problem is a bit tricky, but once you find the answer it seems
to be not so bad!  Let's first play around with the equation you gave us.
Let's multiply by 2 to get:

x^2 + y^2 = 0

Now, we know that when we square any real number, we get a number greater
than or equal to 0, right? If the real number is not zero, its square is
greater than 0; if the real number is 0, its square is 0.  So, why don't
you consider 4 cases:

Case 1:  x and y are both nonzero

Case 2:  x is nonzero but y is zero

Case 3:  x is zero and y is nonzero

Case 4:  x and y are both zero

This will cover all possible cases, right?  For each case, determine
whether or not there are any x's and y's that will work in your equation.
For example, in Case 1, since x and y are both nonzero, x^2 will be greater
than 0 and y^2 will be greater than 0.  That means x^2 + y^2 will be greater
than 0.  Thus, there are no x's and y's that are both nonzero such that your
equation holds.

Test the other 3 cases, and you will come up with an answer!  If any of this
is confusing, or if you want to check your answer, feel free to write back!

--Sydney, "Dr. Math"
```
Associated Topics:
Middle School Graphing Equations

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