Answer
$\{(3,-1)\}$
Work Step by Step
Graph each line
(plot two points per line, such as the interceptcs)
$ \begin{array}{lllllll}
& & & & & & \\
x+y=2 & & & | & x-y=4 & & \\
x=0 & & y=0 & | & x=0 & & y=0\\
& & & & & & \\
0+y=2 & & x+0=2 & | & 0-y=4 & & x-0=4\\
y=2 & & x=2 & | & y=-4 & & x=4\\
(0,2), & & (2,0) & | & (0,-4) & & (4,0)
\end{array} $
Plot the pairs of points and the accompanying lines.
Determine intersection points, if any.
(see attached image)
There is an intersection point,
the solution set is $\{(3,-1)\}$
