Draw the graphs of the two given equations

The first one is x+y=2. or y= 2-x

x	y
0	2
2	0

Plot the points (0,2) and (2,0) and join to get the line

The next is y-x=2, or y=x+2

x	y
0	2
-2	0

Plot the points (0,2) and (-2,0) and join to get the line

Look for the point at which the lines intersect. Read its coordinates from the graph.

The lines intersect at point (0,2)

Hence the Solution is x=0 and y=2 as shown in the figure below

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