Solving systems by substitutions

Let's take two different equations.

4x+2y=8

7x+3y=-10

(I just came up with these on the spot, so the answers might be strange but i should be able to explain nevertheless)

First, let's solve the first equation for "y".

4x+2y=8

-4x - 4x

2y=8-4x

/2

y=4-2x

Now that we have "y", let's plug it into the second equation.

7x+3 (4-2x) = - 10

7x+12-6x=-10

x+12=-10

-12 - 12

x=-22

Alright, now we have "x" definitively, let's plug it in to find "y".

4 (-22) + 2y=8

-88+2y=8

+88 + 88

2y=96

/2

y=48

So from this example you can see. You solve one variable in terms of another (solve y as being 4-2x), plug it into the second equation to find one variable's value, then plug that variable's value back in again later to get the first variable's value.