Answer
$\left\{\begin{array}{l}
x+y=5\\
x-y=-9
\end{array}\right.$
(sample answer)
Work Step by Step
The simplest system of equations with $(-2,7)$ as the only solution would be
$\left\{\begin{array}{l}
x=-2\\
y=7
\end{array}\right.$
Graphically: the intersection of a vertical and horizontal line.
For more sophisticated answer,
find two line equations that pass through $(-2,7)$
For example
$\left\{\begin{array}{l}
x+y=...\\
x-y=...
\end{array}\right.$
Substitute x=-2 and y=7 to find the "correct" RHS's:
$-2+7=5$
$-2-7=-9$
$\left\{\begin{array}{l}
x+y=5\\
x-y=-9
\end{array}\right.$
(sample answer)
