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# How would I solve this simultaneous equation? watch

1. (Original post by JackT2000)
2x + 5y = 16 (1)

Check
2x + 5(2) = 16
2x + 10 = 16
- 10 -10

2x = 6
/2 / 2

x = 3
Yep, x=3 and y=2 are your solutions and answers to the question. All done.
2. (Original post by RDKGames)
Yep, x=3 and y=2 are your solutions and answers to the question. All done.
Thank you simultaneous equations are so tedious
3. (Original post by JackT2000)
Thank you simultaneous equations are so tedious
Just practice them and you'll get a hang of them thus do them quicker too, they don't get any more complicated than this.
4. (Original post by RDKGames)
Just practice them and you'll get a hang of them thus do them quicker too, they don't get any more complicated than this.
Ok thanks and when it comes to taking one equation away from another is it always taking away?
5. (Original post by JackT2000)
Ok thanks and when it comes to taking one equation away from another is it always taking away?
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.
6. (Original post by RDKGames)
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.
So if the signs are different you add and if the same you subtract?
7. (Original post by JackT2000)
So if the signs are different you add and if the same you subtract?
Yes.
8. (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
9. (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.
10. That would confuse me could you give me an example to try
(Original post by RDKGames)
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 the outcome.
11. (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.

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

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

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

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

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

12. (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.
13. (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.
14. (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/ono0irvomy...ions.pptx?dl=0

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