Answer
a) Yes, the point $\left( 4,-1 \right)$ satisfies the equation $x+2y=2$.
b) Yes, the point $\left( 4,-1 \right)$ satisfies the equation $x-2y=6$.
Work Step by Step
(a).
Consider the point $\left( 4,-1 \right)$ as $\left( x,y \right)$.
Now put $x=4$ and $y=-1$ to satisfy the equation $x+2y=2$.
$\begin{align}
& x+2y=2 \\
& 4+2\left( -1 \right)=2 \\
& 4-2=2 \\
& 2=2
\end{align}$
Hence, the $\left( 4,-1 \right)$ satisfies $x+2y=2$.
(b).
Consider the point $\left( 4,-1 \right)$ as $\left( x,y \right)$.
Now put $x=4$ and $y=-1$ to satisfy the equation $x-2y=6$.
$\begin{align}
& x-2y=6 \\
& 4-2\left( -1 \right)=6 \\
& 4+2=6 \\
& 6=6
\end{align}$
Hence, the $\left( 4,-1 \right)$ satisfies $x-2y=6$.
