i do not understand how to get the answer to my problems 1) y=-2x+6 y=2x+2

You are given a "system of equations"

y=-2x+6

y=2x+2

We can apply the "elimination method" by simply adding both equations together. The idea is get rid of one of the variables. Notice, when we do this, we eliminate the x:

y=-2x+6

y=2x+2

----------

2y = 8

y = 4

Now, to find x, we substitute the above back into either of the two original equation (pick the simpler one):

y=2x+2

4=2x+2

2 = 2x

1 = x

Answer: x=1 and y=4