Simultaneous equations

Hi guys

Quite a simple question if anyone can help. Do you alway have to put varibles on one side and contents on the other? When using the elimination method that is.

For example y=x-3, 2y=x+5 you wouldn't have to move all varibles to one side

Here your variables are x and y. You normally group all like variables together to simplify the expression. And in both equations, keep the variable you want to eliminate on one particular side. So the way you've written it is fine. If you did equation 2 minus equation 1, you eliminate x and you get y = 8.

The basic concept is to eliminate one of the variables. You've got two options to do this: 1. substitution or 2. direct elimination.

Let's say you had:
y = x + 3
2y = 3x + 5

Substitution:

Because you have y on its own in one of the equations, you can substitute it directly into equation 2.
2(x + 3) = 3x + 5
2x + 6 = 3x + 5
6 - 5 = 3x - 2x
x = 1.

then y = x + 3 = 1 + 3 = 4.

Elimination:

The trick is to make one of the variables have the same coefficient (the number in front of the variable) in both equations. Then rearrange so that this variable is only on particular side of the equation.

So, let's choose x as the variable to eliminate.
If I multiply all terms of equation 1 by 3, I get
3y = 3x + 9.
The second equation is still
2y = 3x + 5.

If I subtract these two equations I get
3y - 2y = 3x - 3x + 9 - 5
y = 4.

Hope this is clear!

as when your dealing with negative and positive number the order effects the final answer

Hi thank you for this!

Could I just ask you one more thing? I think I've grasped most of it now other then one thing. When you subtract or add the two equations to eliminate one of the varibles how do you determined which order to do them in. So, do you take equation 1 of 2 or 2 from 1? Or in the case you have to rearrange both questions 3 from 4 and vice versus, as when your dealing with negative and positive number the order effects the final answer

I like solving simultaneus equations

I don't. Can you tell?