Answer
$(5,1)$
Work Step by Step
For each equation plot x- and y-intercepts and join with a straight line.
$\left[\begin{array}{lll}
& x-int. & y-int.\\
& y=0 & x=0\\
& & \\
x+y=6 & x=6 & y=6\\
& (6,0) & (0,6)\\
& & \\
x-y=4 & x=4 & -y=5\\
& (4,0) & (0,-5)
\end{array}\right]$
Graphically solving: $x=5,\ y=1$.
Checking:$\qquad \left\{\begin{array}{l}
5+1=6\\
5-1=4
\end{array}\right.$
both equations are satisfied, $(5,1)$ is the solution.