# Solve Math Question: Rearrange Formula to Make y Subject

• WillyVee
In summary, Willy Vee is having trouble answering a question given to her in maths. Rearrange the formula to make y the subject. Any help would be greatly appreciated, as well as the steps taken to get the answer. 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.
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.

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.

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.

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

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symbolipoint said:
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.

cor you sound like a proper bore!...not to be mean or nothing

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nah I'm stuck on some rearrange formula homeowrk - teacher expects me to do it even though i weren't there

fifim007 said:
cor you sound like a proper bore!

...not to be mean or nothing
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.

## What is the purpose of rearranging a formula to make y the subject?

Rearranging a formula to make y the subject allows us to solve for the value of y in terms of the other variables in the equation. This can be useful in solving problems where we need to find the value of y or in simplifying complex equations.

## What are the steps for rearranging a formula to make y the subject?

The steps for rearranging a formula to make y the subject are as follows:
1. Identify the variable you want to make the subject (in this case, y).
2. Isolate the term with y on one side of the equation by performing inverse operations on the other terms.
3. Simplify the equation if necessary.
4. Divide both sides of the equation by the coefficient of y to isolate y.
5. Check your answer by plugging in the value of y into the original equation.

## Can any formula be rearranged to make y the subject?

Yes, any formula can be rearranged to make y the subject as long as it follows the rules of algebra. This means that the same operations must be performed on both sides of the equation to maintain balance.

## What are some common mistakes to avoid when rearranging a formula to make y the subject?

Some common mistakes to avoid when rearranging a formula to make y the subject include:
- Forgetting to perform the same operations on both sides of the equation.
- Making arithmetic errors while simplifying the equation.
- Not isolating y and leaving it with other terms on the same side of the equation.
- Not checking the answer by plugging it back into the original equation.

## Can I use the same steps to rearrange a formula for any variable?

Yes, the steps for rearranging a formula to make y the subject can be applied to any variable. Simply follow the same steps, but instead of isolating y, isolate the variable you want to make the subject.

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