Answer
See below:
Work Step by Step
The provided system of equations is:
\[\begin{align}
& x+y=2 \\
& x-y=4
\end{align}\]
To solve it by graph method, plot the two lines in rectangular coordinate system. Use the following steps:
Step 1:
First graph the line \[x+y=2\].
Find x-intercept, set \[y=0\] in above equation.
\[\begin{align}
& x+y=2 \\
& x+0=2 \\
& x=2
\end{align}\]
Find y-intercept, set \[x=0\]in above equation.
\[\begin{align}
& x+y=2 \\
& 0+y=2 \\
& y=2
\end{align}\]
Plot the ordered pairs \[\left( 2,0 \right)\text{ and }\left( 0,2 \right)\].
Step 2:
Draw a line passing through \[\left( 2,0 \right)\]and \[\left( 0,2 \right)\].
Step 3:
Now graph the line,\[x-y=4\].
Find x-intercept, set \[y=0\] in above equation.
\[\begin{align}
& x-y=4 \\
& x-0=4 \\
& x=4
\end{align}\]
Find y-intercept, set \[x=0\]in above equation.
\[\begin{align}
& x-y=4 \\
& 0-y=4 \\
& y=-4
\end{align}\]
Plot the ordered pairs \[\left( 4,0 \right)\text{ and }\left( 0,-4 \right)\].
Step4:
Draw a line passing through \[\left( 4,0 \right)\]and \[\left( 0,-4 \right)\].
Step5:
From the graph, point of intersection is \[\left( 3,-1 \right)\].
To ensure that the graph is accurate, check the point of intersection \[\left( 3,-1 \right)\]in both equations.
\[\begin{align}
& x+y=2 \\
& 3+\left( -1 \right)=2 \\
& 3-1=2 \\
& 2=2
\end{align}\]
\[\begin{align}
& x-y=4 \\
& 3-\left( -1 \right)=4 \\
& 3+1=4 \\
& 4=4
\end{align}\]
Coordinates of the point of intersection \[\left( 3,-1 \right)\]that satisfy both the equations.
Hence, the graph of the system of equations is correct.
