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# Simultaneous equations Watch

1. 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
2. (Original post by CheeseMunchies)
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.
3. (Original post by superduper9)
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.
If one of them was 2x then would you have to move all varibles? I'm just trying to be clear when you have to rearrange and when is ok not to.

Is it just when there are not varibles the add or subtract to make 0 between the two equations?

And thanks for the help
4. 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!
5. (Original post by superduper9)
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!
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
6. (Original post by CheeseMunchies)
as when your dealing with negative and positive number the order effects the final answer
This is not the case

You can add or subtract in either order and the answer will be the same
7. (Original post by CheeseMunchies)
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
You can subtract them in any order: either equation 2 minus equation 1 or equation 1 minus equation 2. The order won't affect the final answer.

For example:
3y = 3x + 9
2y = 3x + 5

If I did 1 minus 2 I get
3y - 2y = 3x + 9 - 3x - 5
y = 4.

If I did 2 minus 1 I get
2y - 3y = 3x + 5 - 3x - 9
-y = -4
y = 4.
8. I like solving simultaneus equations
9. (Original post by German123)
I like solving simultaneus equations
I don't. Can you tell?
10. (Original post by CheeseMunchies)
I don't. Can you tell?
Nope but remember a simultaneus equation came up on my math exam. If you need help with the sim equations feel free to PM me.

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