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# How to solve simultaneous equations that have signs in front of the first coefficient watch

1. For example I can solve this:

3x + 7y = 26
4x + 5y = 13

The signs are the same so once I make the coefficients of x
the same I will Subtract the top equation from the bottom. SSS = Subtract if signs same

Now say If it was like this instead how would I solve it?? :

-3x + 7y = 26
+4x + 5y = 13
2. Multiply the first equation by 4 and the second one by 3. Can you see that the coefficient of x in both equation is the same. Solve by elimination from there.
3. You'd make the coefficients equal like before then you'd add the two equations instead of subtracting them, which will make the x's cancel out and disappear.
4. (Original post by JackT2000)
For example I can solve this:

3x + 7y = 26
4x + 5y = 13

The signs are the same so once I make the coefficients of x
the same I will Subtract the top equation from the bottom. SSS = Subtract if signs same

Now say If it was like this instead how would I solve it?? :

-3x + 7y = 26
+4x + 5y = 13
If the signs are both plus or both minus, then subtract.
If the signs are plus and minus, then add.

-3x + 7y = 26 (1)
4x + 5y = 13 (2)

Let's make the y values the same by multiplying (1) by 5 and (2) by 7.

This gives us:

-15x + 35y = 130 (3)
28x + 35y = 91 (4)

As the y signs in equations (3) and (4) are both plus, we subtract.

-15x - 28x + 35y - 35y = 130 - 91

-43x = 39

x = -39/43, then sub that into equation (1) or (2) to find y.
5. Don't remember 'rules', try and understand what you're doing and why you're doing it and how it works.
6. (Original post by B_9710)
Don't remember 'rules', try and understand what you're doing and why you're doing it and how it works.
This. Cannot stress this enough.
7. (Original post by jake4198)
If the signs are both plus or both minus, then subtract.
If the signs are plus and minus, then add.

-3x + 7y = 26 (1)
4x + 5y = 13 (2)

Let's make the y values the same by multiplying (1) by 5 and (2) by 7.

This gives us:

-15x + 35y = 130 (3)
28x + 35y = 91 (4)

As the y signs in equations (3) and (4) are both plus, we subtract.

-15x - 28x + 35y - 35y = 130 - 91

-43x = 39

x = -39/43, then sub that into equation (1) or (2) to find y.
So we ignore the signs in front of the first coeficciant until we eliminate
8. (Original post by B_9710)
Don't remember 'rules', try and understand what you're doing and why you're doing it and how it works.
What do you mean by rules? I'm sure must people think of it as if the signs are the same you subtract and different add? Please correct me if I'm wrong
9. (Original post by JackT2000)
So we ignore the signs in front of the first coeficciant until we eliminate
The sign on the front of the coefficient is completely irrelevant.
10. (Original post by jake4198)
The sign on the front of the coefficient is completely irrelevant.
Ok thanks. Is it ok to remember add if the signs are different and subtract if they are the same? Will it always work?
11. (Original post by JackT2000)
Ok thanks. Is it ok to remember add if the signs are different and subtract if they are the same? Will it always work?
Just think about what manipulations you can do in order to make either both x coefficients or both y coefficients have the same magnitude, then add or subtract them as necessary to remove those terms from the equations.
12. I always found it easier to just move it around. It may take more steps but I know it's correct. So maybe check this and see if it looks easier for you too? You don't have to use it but I always found this one made me understand it rather than remember the rules.

For example.
You multiply your one and get
-12x+28y=104
12x+15y=39

Then you take one and move it around. So let's say we want -12x on the bottom one.

Move Y to the other side.
12x=39-15y (sign changes if you move it to the other side)

Now we need -12x not 12x. So all signs change.
-12x = -39 + 15y

Go back to the original
-12x + 28y = 104
-12x = -39 + 15y
So -12x is same as -39 + 15y. So replace -12x in first one with the stuff after equal in second one.
-39 + 15y +28y = 104

Keep only Y on the left.
15y + 28y = 104 + 39 (sign changes when you move to the other side)

Simplify
43y = 143

Then you'd go through the usual. Get y and put it in to find x.
13. (Original post by JackT2000)
What do you mean by rules? I'm sure must people think of it as if the signs are the same you subtract and different add? Please correct me if I'm wrong
No, nobody who understands what they're doing it thinks of it like that. Like he said, don't try remembering rules, just understand what you're doing. Why is it okay to multiply both sides of the equation by something? Why can we add and subtract equations? Why would we want to do that? Then you don't need to be thinking "hmm, okay step 1: same sign, step 2: subtract step 3:..." without a sliver of understanding what's really going on.
14. (Original post by JackT2000)
What do you mean by rules? I'm sure must people think of it as if the signs are the same you subtract and different add? Please correct me if I'm wrong
The "rules" we're referring to would often be the school's way of teaching you the subject. Simultaneous equations can be taught as subtraction of one equation from another to find a solution to a multivariable, but as you can see it doesn't work all the time.

The other posters mean that you should understand the rationale behind what you're doing, which is really to eliminate a variable so you can solve for the other. The rule that "if the signs are the same then you subtract" and vice-versa is correct, but you're just learning them by rote - if presented with a more difficult question involving a modulus, you'd be stuck.

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