Answer
$\{(0,4)\}$
Work Step by Step
Graph each line
(plot two points per line, such as the interceptcs)
$ \begin{array}{lllllll}
& & & & & & \\
x+y=4 & & & | & y-x=4 & & \\
x=0 & & y=0 & | & x=0 & & y=0\\
& & & & & & \\
0+y=4 & & x+0=4 & | & y-0=4 & & 0-x=4 \\
y=4 & & x=4 & | & y=4 & & x=-4\\
(0,4), & & (4,0) & | & (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 $\{(0,4)\}$
