Originally Posted by

**alexcordero** Hello all,

I understand that the goal is to eliminate one of the variables and not simply add to two equations.

In this example:

Solve the system:

-2x + y = 2

-x + 3y = -4

simplifies to:

-6x - 3y = -6

-x + 3y = -4

I understand that:

-3(-2x + y) = -3(2) = -6x - 3y = -6 by distribution.

But I don't understand why -3 was used and not simply 3?

In other examples in my textbook,

9(3x+4y) = 9(13)

4(5x-9y) = 4(6)

-9 is converted to 9.

So what are you supposed to use? How do you determine what sign the coefficient should keep? The book I'm using simply shows my examples but doesn't explain why the different signs are used.

Thanks.