No, it's not always taking away.

Consider this example:

x+y=1
x-y=1

If you want to eliminate y, then you add both of them as you would get y+(-y) which cancels it out. If you want to eliminate x, then you subtract them as x-x will be 0x as well.

So the simple rule goes as follows when considering the coefficients of the same variable (same sure they're the same number); if it's +/+ then you subtract, if it's +/- then you add, if it's -/- then you subtract. Make a note of this for future problems.

(edited 7 years ago)

Reply 25

2771024

Original post by RDKGames

So if the signs are different you add and if the same you subtract?

Reply 26

RDKGames

Study Forum Helper

Original post by JackT2000

So if the signs are different you add and if the same you subtract?

Yes.

Reply 27

2771024

Original post by RDKGames

Yes.

Just to check can the first coeficciant
Have. A minus or plus in front of it for example

-2x + 5y = 50
-3x + 5y = 20

Reply 28

RDKGames

Study Forum Helper

Original post by JackT2000

Just to check can the first coeficciant
Have. A minus or plus in front of it for example

-2x + 5y = 50
-3x + 5y = 20

Yes it can. -2x+5y is the same as 5y-2x, you can swap them around and that has no effect; it's essentially just deciding what you are doing first, whether multiplying by x first or by y, it doesn't change the outcome.

(edited 7 years ago)

Reply 29

2771024

That would confuse me could you give me an example to try

Original post by RDKGames

Reply 30

RDKGames

Study Forum Helper

Original post by JackT2000

That would confuse me could you give me an example to try

Have a go at these. I came up with them and made them sort of increasing in difficulty.

It is also important to note that when you are solving simultaneous equations, you are finding the point of intersection between lines (1) and (2) which is the geometric interpretation of what is happening on the graph; basically the point where the two lines meet.

4x+3y=2

x+2y=3

------------------------------------

x+2y=2

3x-y=20

------------------------------------

2x-y=5

x-3y=5

------------------------------------

2x-y=2

-3x+2y=1

------------------------------------

-2x-y=2

3x+4y=2

------------------------------------
For this one, I want you to think about sketching these two lines and attempt to explain what is going on:

y-x=1

3y-3x=6

(edited 7 years ago)

Reply 31

B_9710

Original post by JackT2000

So if the signs are different you add and if the same you subtract?

Don't just parrot lean rules. Understand what you're doing and why it works.

Reply 32

RDKGames

Study Forum Helper

Original post by B_9710

Don't just parrot lean rules. Understand what you're doing and why it works.

Believe me, at his stage it's better to just follow the rules rather than spend an eternity and attempt to understand it by the looks of it. He'll just keep following these rules and eventually it will click to him that these are points of intersections he is finding, that's how it happened with me back at GCSE anyway.

(edited 7 years ago)

Reply 33

MartyO

Original post by JackT2000

That would confuse me could you give me an example to try

Here's an animated PowerPoint I put together with worked examples and different ways to solve simultaneous equations. I've also recapitulated what has been said in this topic.
https://www.dropbox.com/s/ono0irvomyy07sp/Solving%20Systems%20Of%20Linear%20Equations.pptx?dl=0