Answer
$\text{a)
solution
}\\\text{b)
solution
}\\\text{c)
NOT a solution
}\\\text{d)
solution
}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Substitute the given points in the given inequality, $
x-2y\le4
.$ 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}
x-2y\le4
\\\\
0-2(0)\le4
\\\\
0-0\le4
\\\\
0\le4
\text{ (TRUE)}
.\end{array}
Hence, $(
0,0
)$ is a solution.
b) Substituting the given point, $(
2,-1
)$ in the given inequality results to
\begin{array}{l}\require{cancel}
x-2y\le4
\\\\
2-2(-1)\le4
\\\\
2+2\le4
\\\\
4\le4
\text{ (TRUE)}
.\end{array}
Hence, $(
2,-1
)$ is a solution.
c) Substituting the given point, $(
7,1
)$ in the given inequality results to
\begin{array}{l}\require{cancel}
x-2y\le4
\\\\
7-2(1)\le4
\\\\
7-2\le4
\\\\
5\le4
\text{ (FALSE)}
.\end{array}
Hence, $(
7,1
)$ is NOT a solution.
d) Substituting the given point, $(
0,2
)$ in the given inequality results to
\begin{array}{l}\require{cancel}
x-2y\le4
\\\\
0-2(2)\le4
\\\\
0-4\le4
\\\\
-4\le4
\text{ (TRUE)}
.\end{array}
Hence, $(
0,2
)$ is a solution.
\begin{array}{l}\require{cancel}
\text{a)
solution
}\\\text{b)
solution
}\\\text{c)
NOT a solution
}\\\text{d)
solution
}
\end{array}
