# Rearranging Formula

1. Feb 22, 2008

### WillyVee

I am having trouble answering a question given to me in maths:

Rearrange this formula to make y the subject.

ax + by = cx - dy

Any help would be greatly appreciated, plus the steps taken to get the answer.

2. Feb 22, 2008

### symbolipoint

What do you exactly mean, "y the subject"? Are you interested in English grammar, or are you interested in introductory Algebra? you seem to be asking for a formula for y. So your general interest is to practice properties of equality.

use distributive property;
use multiplicative inverse property.

3. Feb 22, 2008

### HallsofIvy

Staff Emeritus
Symbolipoint, "make y the subject of the equation" is "English" English for what us "Ammuricans" would call "solve the equation for y".

Willy Vee, you need to get y by itself on one side of the equation: y= ...

To do that you look at what has been "done to y" and then do the opposite. That is why symbolipoint has three "inverses"!

You have, to start with, ax+ by= cx- dy. You want y only on the left side of the equation and right now there is a "-dy" on the right. Do the opposite- add dy (dy is the "additive inverse of -dy) to both sides: ax+ by+ dy= cx- dy+ dy= cx. You want no x on the left so add -ax to both sides (-ax is the "additive inverse of ax): ax+ by+ dy- ax= by+ dy= cx- ax. You should see that you can now factor y out of the left side: by+ dy= (a+d)y so you really have (a+d)y= cx-ax. If a+ d is not 0, then we can divide both sides by a+d (or multiply by the "multiplicative inverse of a+d, 1/(a+d)) to get
y= (cx- ax)/(a+ d). You might also notice that you can factor an x out of that: [(c-a)/(a+d)]x.

4. Feb 24, 2008

### flebbyman

You left the b out HallsofIvy ;)

First add dy and subtract ax from each side to isolate y on the left.

by+dy=cx-ax

Take a common factor of y from the right side and an x from the left side.

(b+d)y=(c-a)x

y=( (c-a)/(b+d) )x and b+d≠0

Last edited: Feb 24, 2008
5. Oct 14, 2009

### fifim007

cor you sound like a proper bore!

.......not to be mean or nothing

Last edited: Oct 14, 2009
6. Oct 14, 2009

### fifim007

nah i'm stuck on some rearrange formula homeowrk - teacher expects me to do it even though i werent there

7. Oct 14, 2009

### HallsofIvy

Staff Emeritus
You just can't help it?

Ok, so that I don't bore you anymore I will not respond to any more of your questions.

In fact, to be helpful, I will warn others not to give detailed answers to your questions since they bore you.

And, since it was clearly to0 boring for you to read the info you were required to when you registered (in particular the part that says homework must go in the homework section and you must show an effort), I will tell you that here (hope fifim007 got this far before she got bored) and move this to the PreCalculus homework site.