Answer
$(1,4)$ is a solution of the system.
Work Step by Step
The given system of linear inequalities is.
$\Rightarrow y\geq 3x+1$ ...... (1)
$\Rightarrow y\gt x-1$ ...... (2)
Substitute $1$ for $x$ and $4$ for $y$ in each inequality.
Inequality (1)
$\Rightarrow y\geq 3x+1$
$\Rightarrow 4\geq 3(1)+1$
$\Rightarrow 4\geq 3+1$
$\Rightarrow 4\geq 4$
True.
Inequality (2)
$\Rightarrow y\gt x-1$
$\Rightarrow 4\gt 1-1$
$\Rightarrow 4\gt 0$
True.
$(1,4)$ satisfy each inequality.
Hence, $(1,4)$ is a solution of the system.
