Answer
$\text{a)
solution
}\\\text{b)
solution
}\\\text{c)
solution
}\\\text{d)
NOT a solution
}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Substitute the given points in the given inequality, $
y\le1
.$ If the inequality is satisfied, then the given point is a solution. Otherwise, the given point is not a solution.
$\bf{\text{Solution Details:}}$
a) Substituting the given point, $(
0,0
)$ in the given inequality results to
\begin{array}{l}\require{cancel}
y\le1
\\\\
0\le1
\text{ (TRUE)}
.\end{array}
Hence, $(
0,0
)$ is a solution.
b) Substituting the given point, $(
3,1
)$ in the given inequality results to
\begin{array}{l}\require{cancel}
y\le1
\\\\
1\le1
\text{ (TRUE)}
.\end{array}
Hence, $(
3,1
)$ is a solution.
c) Substituting the given point, $(
2,-1
)$ in the given inequality results to
\begin{array}{l}\require{cancel}
y\le1
\\\\
-1\le1
\text{ (TRUE)}
.\end{array}
Hence, $(
2,-1
)$ is a solution.
d) Substituting the given point, $(
-3,3
)$ in the given inequality results to
\begin{array}{l}\require{cancel}
y\le1
\\\\
3\le1
\text{ (FALSE)}
.\end{array}
Hence, $(
-3,3
)$ is NOT a solution.
Hence,
\begin{array}{l}\require{cancel}
\text{a)
solution
}\\\text{b)
solution
}\\\text{c)
solution
}\\\text{d)
NOT a solution
}
\end{array}