What is the solution set of the system? x-y=4 x+y=2

You can just add these to functions together to cancel out y to start with.

(x-y=4)+(x+y=2)

2x=6  divide both sides by 2

x=3, which makes x+y=2 become:

3+y=2

y=-1

So the solution to the system of equations is the point (3,-1)

Our current equations are:
X - Y = 4
X + Y = 2
Given x subtracting y gives us a larger number than they are added, X must be a larger number, and Y must be negative or a lower number than X.
Let's try -1 and 3.
3 - (-1) = 4, as subtracting a negative makes a positive.
3 + (-1) = 2, as adding a negative to a positive is subtracting a positive.
x = 3
y = -1
I hope this helps!