Question

How can you find solutions for equations with two variables?

Answer 1

as in ax+by=c and dx+ey=f?

Answer 2

i think so...

Answer 3

Do you have an exact problem?

Answer 4

no

Answer 5

Alright so lets say you have x+y=10 and 3x+2y=22

There are a couple different ways to solve a system of two variables.

The first one is called substitution in which you solve one equation for one of the variables

So the first equation I will solve for y yielding y=10-x

You next substitute the 10-x term into the second equation wherever you see a y

This will give you 3x+2(10-x)=22 which you then can easily solve for x [x=2]

With that you would plug the x=2 back into your original number 1 to get y=10-2=8

Answer 6

The next method is elimination in which you try to get ride of one of the variables. In this method, you want to get one of the terms (x or y) to be the opposite (ie 3x in the first and -3x in the second, or -2y in the first and 2y in the second)

You can do this by multiplying one (or both) of the equations by a constant.

For the x+y=10 and 3x+2y=22 I will eliminate the x by multiplying the first equation by a -3

This yields -3x-3y=-30

When you add this new equation to the original second, you obtain 3x+2y-3x-3y=22-30 which simplifies to -y=-8 or y=8

You can then put y=8 back into one of the originals as in substitution to obtain your x value of 2 for this problem

Answer 7

Did that help you?