#### Answer

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#### Work Step by Step

To get the point of intersection of the equations $x+2y=2$ and $x-2y=6$, first plot the graph with some steps which are as follows.
Put $x=0$ and get the y-intercept for $x+2y=2$.
$\begin{align}
& x+2y=2 \\
& 0+2y=2 \\
& 2y=2 \\
& y=1
\end{align}$
Hence, the graph passes through the point $\left( 0,1 \right)$.
Put $y=0$ and get the x-intercept for $x+2y=2$.
$\begin{align}
& x+2y=2 \\
& x+2\times 0=2 \\
& x=2
\end{align}$
Hence the graph passes through the point $\left( 2,0 \right)$.
Again,
Put $x=0$ and get the y-intercept for $x-2y=6$.
$\begin{align}
& x-2y=6 \\
& 0-2y=6 \\
& -2y=6 \\
& y=-3
\end{align}$
Hence the graph passes through the point $\left( 0,-3 \right)$.
And put $y=0$ and get the x-intercept for $x-2y=6$.
$\begin{align}
& x-2y=6 \\
& x-2\times 0=6 \\
& x=6
\end{align}$
Thus, the graph passes through the point $\left( 6,0 \right)$.
Now, plot the graph of the equations $x+2y=2$ and $x-2y=6$, and get the intersection point.