# How to Solve for a Variable

••• d3 Dan @ flickr: http://www.flickr.com/photos/acidwashphotography/2967752733/
Print

Solving for the variable in a math problem isn't as hard as some may think (thanks to the elimination method that is!) Here are step by step instructions of how it's done.

The first thing you'll want to do is critique the problem. What are you being asked to solve for? Once you understand that you can move on.

Let's say you're being asked to solve for y and the problem looks like this: 16x+4y=20. Basically what's being asked here is to get all the numbers on the other side of the equal sign so that y is by itself, i.e. y=(all the other things you've put on the other side of the equal sign).

Begin by subtracting the number that's being added to 4y. In this case that number would be 16x (the variable, x, goes with it the number too, remember that) So after you've subtracted 16x your problem should look like this:

4y=20-16x

Now you've made the problem a bit easier. It might look like you're done but ask yourself, "Is y totally by itself?" No it is not, there's a 4 clinging to it! So now we need to get 4 to the other side of the equal sign as well which will finally leave y by itself.

What you'll need to do now is divide the 4 into both side of the equation. The 4/4 in front of the y's will cancel out and become 1y (at this point, the 1 turns invisible so that all you'll see is y, the one will always be there, but consider it invisible). So now all you have to do is divide 4 into 20+16x. You will get: y=5-4x

And now your problem is solved. You've not only gotten all the other numbers to the other side of the equal sign, but you've reduced those numbers by dividing them by 4.

#### Things You'll Need

• Math problem with a variable in it.
• pencil
• papper