Associated Topics || Dr. Math Home || Search Dr. Math

### Unique Values for x, y

```
Date: 9/10/96 at 16:46:45
From: Anonymous
Subject: Values for x, y Such That...

What are unique values for x and y so that x+y and y*x equal the
same number?

Thanks.
```

```
Date: 9/10/96 at 19:56:40
From: Doctor Mike
Subject: Re: Values for x, y Such That...

Hello,

I can think of 2 solutions quickly, namely X = 0, Y = 0 and
X = 2, Y = 2.

Are you looking for solutions with different values for X and Y?
You could take X = 3 and Y = 3/2 .  There are many other solutions.
If you are curious how I know that, read on.

In order for X+Y and X*Y to equal the same number they have to equal
each other, so you have the equation X*Y=X+Y. You can solve for Y in
terms of X to better understand this. The first step is to subtract
Y from both sides to get X*Y-Y=X. The next step is to factor the left
side to get (X-1)*Y=X. Then divide both sides by (X-1) to get
Y=X/(X-1).  This says you can select almost any value for X, and the
formula will give you a Y that works with that X. The only forbidden
X value is one (1), which makes the denominator zero.

A solution that is a little farther out is Y=1.01 and X=101.
If you know about graphing equations, this is an interesting one!

I hope this helps.

-Doctor Mike,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/
```
Associated Topics:
Middle School Algebra

Search the Dr. Math Library:

 Find items containing (put spaces between keywords):   Click only once for faster results: [ Choose "whole words" when searching for a word like age.] all keywords, in any order at least one, that exact phrase parts of words whole words

Submit your own question to Dr. Math
Math Forum Home || Math Library || Quick Reference || Math Forum Search