Answer
$(0,0)$ is not a solution of the system.
Work Step by Step
The given system of linear inequalities is.
$\Rightarrow y\leq x+7$ ...... (1)
$\Rightarrow y\geq 2x+3$ ...... (2)
Substitute $0$ for $x$ and $0$ for $y$ in each inequality.
Inequality (1)
$\Rightarrow y\leq x+7$
$\Rightarrow 0\leq 0+7$
$\Rightarrow 0\leq 7$
True.
Inequality (2)
$\Rightarrow y\geq 2x+3$
$\Rightarrow 0\geq 2(0)+3$
$\Rightarrow 0\geq 0+3$
$\Rightarrow 0\geq 3$
False.
$(0,0)$ does not satisfy each inequality.
Hence, $(0,0)$ is not a solution of the system.
