# Thread: Rule of sim eqs?

1. ## Rule of sim eqs?

Hello.

When eliminating the x or ys is their a rule for which you take awy from each other when the signs are different.

example

equation
A
B

becomes
C
D

Do you always take the larger number away? always take the C away from D or vice versa? or is it determined by the multipliers used in A nd B originally?

C-D or D-C or does it change?

Thanks
Roger

2. Originally Posted by rogerroger
Hello.

When eliminating the x or ys is their a rule for which you take awy from each other when the signs are different.

example

equation
A
B

becomes
C
D

Do you always take the larger number away? always take the C away from D or vice versa? or is it determined by the multipliers used in A nd B originally?

C-D or D-C or does it change?

Thanks
Roger
It depends. For examply:

x+y = 5 (1)
x-y = 4. (2)

If you wanted to get rid of the xs, then you subtract 1 from 2, OR subtract 2 from 1 since both xs are positive in both equations. When you have two positive numbers, and you want to get 0, then you have to subtract one from the other.

To get rid of the ys you have to ADD (1) to (2), OR subtract (2) from (1), because one is positive and one is negative. When you have 1 negative number, one positive number, you have to subtract the negative from the positive, or add the negative to the positive.

In another example:

x-y = 5 (1)
-x-y = 4 (2)

Here, if you want to get rid of the xs, you use the rules from above! But if you want to get rid of ys, then you have to subtract (1) from (2), OR (2) from (1), since they are both negative.

And indeed, if you had two equations in which x and y have different coefficients, then you multiply both or one of the equations by whatever is necessary to get a common coefficient.

3. Don't memorize "rules"- think about what you are doing.

If I see the equations, x+ 2y= 4 and 3x- 2y= 5, I would notice that "y" in the first equation has coefficient 2 and "y" in the second has coefficient -2 and so if I add, 2y+ (-2y)= 0, I eliminate the "y". Adding the two equations gives x+ 3x+ 2y- 2y= 4+ 5 or 4x= 9. If I had different numbers I could multiply by other numbers perhaps in order to be able to eliminate a variable. But the important thing is to think about the result I want to achieve, a single equation with only one variable, rather than think about a "rule" I have to follow.

Mathematics has a lot of rules it is easy to follow blindly. But mathematics is about ideas, not rules.