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# Simultaneous equations

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1. How would I solve this ?

2x + 3y = 19
-2x + y = 1

The signs are the same so do I do (1) - (2)
2. (Original post by JackT2000)
How would I solve this ?

2x + 3y = 19
-2x + y = 1

The signs are the same so do I do (1) - (2)
You have +2x in the first one and -2x in the second one. You'd add them to rid the x and then solve it for y.
3. 2--2=4
To eliminate x you need to add the two equations.
4. (Original post by Potatoo)
You have +2x in the first one and -2x in the second one. You'd add them to rid the x and then solve it for y.
But if when the signs are the same you subtract and when they are different you add?
5. (Original post by JackT2000)
But if when the signs are the same you subtract and when they are different you add?
Yes that is right.
6. (Original post by LifeIsFine)
2--2=4
To eliminate x you need to add the two equations.
So do I add the first equation to the second equation?
7. (Original post by JackT2000)
So do I add the first equation to the second equation?
(Original post by JackT2000)
But if when the signs are the same you subtract and when they are different you add?
You only consider this depending on which variable you are attempting to eliminate, and the quantity of the variable needs to be the same in both equations. The signs of x are the different and the quantity's the same so you add them together.

No point in remembering rules if you don't understand why something is happening.
8. It doesn't matter what equation you add you'll get the same answer:
2x + 3y = 19
-2x + y = 1 WHEN YOU ADD YOU WILL GET RID OF THE 2X AND THE - 2X. think of it being -2+2=0

Then you will be left with

4y = 20 SINCE WE ARE ADDING. NOW DIVIDE BOTH SIDES BY 4
y= 5 NOW TO GET x SUB IN Y=5 IN EITHER EQUATION AND YOU SHOULD GET x = 2
Hope this helps a bit better
9. (Original post by RDKGames)
You only consider this depending on which variable you are attempting to eliminate. The signs of x are the same so you subtract.

No point in remembering rules if you don't understand why something is happening.
So how would I show this on paper?
10. (Original post by JackT2000)
So how would I show this on paper?
Add the two equations and show how the x variable disappears from this operation.
11. (Original post by RDKGames)
Add the two equations and show how the x variable disappears from this operation.

What I mean is how would I show this as I am adding the x variables together and taking away the y variables from each other
12. (Original post by JackT2000)

What I mean is how would I show this as I am adding the x variables together and taking away the y variables from each other
Why are you subtracting the y variables?
13. (Original post by RDKGames)
Why are you subtracting the y variables?
Because the signs are the same for the y variables. You subtract if the signs are the same ?
14. (Original post by JackT2000)
Because the signs are the same for the y variables. You subtract if the signs are the same ?
So what? You clearly don't understand the concept then.

The only reason why you're adding is to make the x's cancel, we don't consider the y's at this point, doesn't matter what their signs are. We are only interesting in the signs of the x variable since that's the one we are eliminating.
15. (Original post by JackT2000)
How would I solve this ?

2x + 3y = 19
-2x + y = 1

The signs are the same so do I do (1) - (2)
first term: 2x + -2x = 0
second term: 3y + y = 4y
third term: 19 + 1 = 20
Overall: 4y = 20
so y = 20/4 (divided)
>>> y = 5
16. You need to add the equations together so you get 4y=20 and you can solve it from there.

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