# Thread: Simple algebra question, solve for the variable

1. ## Simple algebra question, solve for the variable

I'm a little rusty here (or possibly losing my mind at this point), but actually this question involves a bigger problem (substitution rule/calculus) but I'm trying to understand a simple algebra concept first. See the following:

y = 2;
x = 10;

x/y = 5

Ok. I want to solve for y now. Exactly how is this done in algebra? What do you divide or multiply both sides by? I know the answer is y = 1/5x, but I'm unsure as to how one would get to that.

The only way I could see it is to solve for x first:

x = 5y, and then divide 5 on both sides: x/5 = y. There must be an easier and non redundant way, correct?

2. Uhm, you just said it, y = 2

But to solve $\frac{x}{y} = 5$, you can rearrange as follows :

>> For $x$ :

$\frac{x}{y} = 5$

$\frac{x}{y} \times y = 5 \times y$

$\frac{x \times y}{y} = 5 \times y$

$\frac{x}{1} = 5 \times y$ (cancel out the $y$)

$x = 5 \times y$

$x = 5y$

>> For $y$ :

$\frac{x}{y} = 5$

$\frac{y}{x} = \frac{1}{5}$ (inverse on both sides)

$\frac{y}{x} \times x = \frac{1}{5} \times x$

$\frac{xy}{x} = \frac{x}{5}$

$\frac{y}{1} = \frac{x}{5}$ (cancelling out)

$y = \frac{x}{5}$

$y = \frac{1}{5} x$

This is how I would do it (the long way of course, in real situations I would spare most steps). Does it make sense ?

3. Originally Posted by Bacterius
Uhm, you just said it, y = 2

But to solve $\frac{x}{y} = 5$, you can rearrange as follows :

>> For $x$ :

$\frac{x}{y} = 5$

$\frac{x}{y} \times y = 5 \times y$

$\frac{x \times y}{y} = 5 \times y$

$\frac{x}{1} = 5 \times y$ (cancel out the $y$)

$x = 5 \times y$

$x = 5y$

>> For $y$ :

$\frac{x}{y} = 5$

$\frac{y}{x} = \frac{1}{5}$ (inverse on both sides)

$\frac{y}{x} \times x = \frac{1}{5} \times x$

$\frac{xy}{x} = \frac{x}{5}$

$\frac{y}{1} = \frac{x}{5}$ (cancelling out)

$y = \frac{x}{5}$

$y = \frac{1}{5} x$

This is how I would do it (the long way of course, in real situations I would spare most steps). Does it make sense ?
You went all out.