# Thread: Reasoning behind Solving using Substitution

1. ## Reasoning behind Solving using Substitution

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 ?

2. ## Re: Reasoning behind Solving using Substitution

When you solve for y= 5- 2x, you are just saying that "y" and "5- 2x" are the same thing. Whatever you do to one, you can do to the other. The first equation says that if you multiply y by 3 and add 4x, you get -8. Since y is the same as 5-2x, if you multiply 5-2x by 3 and add 4x, you still get -8: 4x+ 3y= 4x+ 3(5- 2x)= 4x+ 15- 6x= 15- 2x= -8

3. ## Re: Reasoning behind Solving using Substitution

Thanks for the reply. I'm afraid I'm still not there.

I don't seem to get why I can use the "Y" of ANOTHER equation for one equation. Maybe I still don't have a clear picture of the relationship between the two seperate equations..

The only thing you are doing when 'solving' this system of equations is finding the intersection of the lines right?

4. ## Re: Reasoning behind Solving using Substitution

At the point of intersection, the y value will be the same for both equations. this is the fundamental concept.

5. ## Re: Reasoning behind Solving using Substitution

The whole point of "simultaneous equations" is that you are seeking values of x and y that will satisfy both equations. The same y must satisfy both equations.