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Verified Answer :

to solve for the variables y and x we substitute the second equation into the first meaning that y = -x +2 you substitute y for (-x+2)
so

(-x +2) = x +4
add x to both sides
2 = 2x + 4 
subtract 4 from both sides
-2 = 2x
divide by 2
-1 = x

now plug x back into the original equation

y = (-1) + 4
y = 3

and 

y = -(-1) + 2
y = 1 +2
y = 3

there you have it x = -1 and y = 3

Hope this helps ;)

to solve what you need to do is 
if y=x+4
and y=-x+2 so both equations have to equal the same thin so 
x+4=-x+2
combine like terms and you get x=-x-2
then next equals 2x=-2
divide by 2 and last you get x=-1