Here are a pair of simultaneous equations:

  x +   y = 3
2x + 3y = 7

How do we find out what both x and y are?

First of all we try to get rid of either the x's or the y's (take your pick - whichever's easiest!)

I'll choose x. To get rid of x we first multiply the first equation by 2 (this will give us 2x in both equations):

2x + 2y = 6
2x + 3y = 7

Now, we subtract one equation from the other (again take your pick - however I'll subtract the first one from the second one to avoid any of those nasty negative numbers!)

This gives us: 3y - 2y = 7 - 6

Which is: 3y - 2y = 1 and as three of something minus two of something leaves you with one of something, this is the same as y = 1.

Now we know that y = 1, all we do is substitute this back into one of the equations (again take your pick). I'll choose the first equation as it looks easiest:

2x + (2 x 1) = 6

or 2x + 2 = 6

Subtracting 2 from both sides gives us 2x = 6 - 2

Or 2x = 4

Now divide both sides by 2 to give x = 2.