Question

walk me through this please
Solve the following system using elimination:

2x+4y=8

3x+5y=15

Answer 1

So in elimination what you do is add both equations together. Since both things on either side of an equation are equal, you can just add each side of the equation to each side of the other equation. For instance lets look at this:

4=4
3=3

I can add them to be
3+4=3+4

Or we can add in variables and say

2x=4
3y=8

2x+3y=4+8

This is possible because when we have any equation we can do the same thing to both sides and it doesn't change a thing, just like 2=2 add 1 to both sides you get 3=3.

Now the point of elimination is to add them together so that one of the variables cancels out.

So if we have

3x+4=y
-x+y=5

we can add them together but none of the variables cancel out. So in this example multiply both sides of the bottom equation by 3.

3x+4=y (same equation, unchanged)
-3x+3y=15 (multiplied both sides by 3)

See how if we add them now the -3x and +3x will become 0?

3x+4-3x+3y=15+y

reduces to

4+3y=15+y

and of course now we can simplify by using normal algebra since we have one variable to solve for. I can give more examples if you like. =D