Answer
\[\left\{ \begin{align}
& y-x=9 \\
& y+x=5 \\
\end{align} \right.\]
Work Step by Step
The slope of a line can be determined when a line passes a point\[\left( {{x}_{1}},{{y}_{1}} \right)\]by
\[m=\frac{y-{{y}_{1}}}{x-{{x}_{1}}}\]
For a system of linear equation having \[\left\{ \left( -2,7 \right) \right\}\] as solution set, the lines must pass through the provided point, having different slopes.
Substituting \[x=-2\] and \[y=7\] in the slope-point form:
\[m=\frac{y-7}{x+2}\]
Let \[m=1\]:
\[\begin{align}
& 1=\frac{y-7}{x+2} \\
& x+2=y-7 \\
& y-x=9
\end{align}\]
Let \[m=-1\]:
\[\begin{align}
& -1=\frac{y-7}{x+2} \\
& -x-2=y-7 \\
& y+x=5
\end{align}\]
Hence, the system of equation is
\[\left\{ \begin{align}
& y-x=9 \\
& y+x=5 \\
\end{align} \right.\]
