The x in equation 1 will add to the -x in equation 2 to get
x+(-x) = 1x+(-1x) = 1x-1x = (1-1)x = 0x = 0
in short, they add and cancel out. The x terms go away.
Apply the same logic to every other term
y terms: y+y = 2y
terms on the right side: 4+2 = 6
So after adding the equations straight down, we end up with
2y = 6
which becomes
y = 3
after we divide both sides by 2
Now that we know y = 3, we can use this to find x. Pick any equation with x and y in it. Say equation 1
x+y = 4
x+3 = 4 ... replace y with 3
x+3-3 = 4-3
x = 1
So the solution is x = 1 and y = 3
Put together, the ordered pair is (1,3) which is visually where the two lines intersect.
Side note:
x+y = 4
1+3 = 4
4 = 4
also,
-x+y = 2
-1+3 = 2
2 = 2
both equations are confirmed
