Answer
$(1,-1)$ is a solution of the system.
Work Step by Step
The given system of linear inequalities is.
$\Rightarrow y \gt -2$ ...... (1)
$\Rightarrow y \gt x-5$ ...... (2)
Substitute $1$ for $x$ and $-1$ for $y$ in each inequality.
Inequality (1)
$\Rightarrow y \gt -2$
$\Rightarrow -1 \gt -2$
True.
Inequality (2)
$\Rightarrow y \gt x-5$
$\Rightarrow -1 \gt 1-5$
$\Rightarrow -1 \gt -4$
True.
$(1,-1)$ satisfy each inequality.
Hence, $(1,-1)$ is a solution of the system.
