Is y the Same on Both Sides?

Date: 9/4/96 at 19:45:45
From: Anonymous
Subject: What Does y Mean?

3/4 + y = 0.75 + y

I thought maybe the y would be the same on both sides, but I'm 
not too sure. 

Date: 9/4/96 at 20:7:48
From: Doctor Tom
Subject: Re: What Does y Mean?

I assume that you're trying to solve the equation above.

If so, it converts to y = y (subtract 3/4 from both sides).

Every y is a solution to this problem.

Just because an equation is written down doesn't mean that there is 
only one answer to it.  Sometimes there aren't any, and sometimes 
there is more than one. In this case, there is an infinite number.

Part of what you learn in algebra is how to figure out if there are 
answers, and if so, how many, and what they are.

Here's an equation with no answers:

    x = x + 1.

There are no numbers that stay the same when you add 1 to them.

Here's an equation with two answers:

   x^2 -3x +2 = 0

(By "x^2", I mean "x squared", or x multiplied by itself.)

Try x = 1:

   1^2 - 3 + 2 = 1 - 3 + 2 = 0

or try x = 2:

   2^2 - 3x2 + 2 = 4 - 6 + 2 = 0

both x = 1 and x = 2 are solutions.

In many cases in beginning algebra, there is only one answer because 
they usually want to start you off with easy problems, but as you can 
see, it is not always the case that there's just one answer!

-Doctor Tom,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/