Hello all, I'm brushing up my basic Math knowledge. Sometimes I have a hard time really understanding why things work the way they do. Now it's in the topic of Systems of Equations: Substitution method.

Untill the graphing method it seemed all very clear to me. You have 2 lines (equations) and you are looking for the intersection point. Clear!

Then comes the substitution method: I know how to use it. I can get to the right answers. But I just don't seem to see, get, or understand why this works.

Example:

4x + 3y = -8

2x + y = 5

Step 1: solve for one variable. So I make: y = 5 - 2x. Clear.

Step 2: Fill in other equation: 4x + 3 (5 - 2x) = -8. I don't seem to really get it from this part...

Can someone provide me with the simple breakthrough insight ?