Answer
See below:
Work Step by Step
The provided system of equations is:
\[\begin{align}
& y=x+5 \\
& y=-x+3
\end{align}\]
To solve it by graph method, plot the two lines in rectangular coordinate system. Use the following steps:
Step 1:
First graph the line \[y=x+5\].
Find x-intercept, set \[y=0\] in above equation.
\[\begin{align}
& y=x+5 \\
& 0=x+5 \\
& x=-5
\end{align}\]
Find y-intercept, set \[x=0\]in above equation.
\[\begin{align}
& y=x+5 \\
& y=0+5 \\
& y=5
\end{align}\]
Plot the ordered pairs \[\left( -5,0 \right)\text{ and }\left( 0,5 \right)\].
Step2:
Draw a line passes through \[\left( -5,0 \right)\]and \[\left( 0,5 \right)\].
Step3:
Now graph the line,\[y=-x+3\].
Find x-intercept, set \[y=0\] in above equation.
\[\begin{align}
& y=-x+3 \\
& 0=-x+3 \\
& x=3
\end{align}\]
Find y-intercept, set \[x=0\]in above equation.
\[\begin{align}
& y=-x+3 \\
& y=0+3 \\
& y=3
\end{align}\]
Plot the ordered pairs \[\left( 3,0 \right)\text{ and }\left( 0,3 \right)\].
Step4:
Draw a line passes through \[\left( 3,0 \right)\]and \[\left( 0,3 \right)\].
Step5:
From the graph, point of intersection is \[\left( -1,4 \right)\].
To ensure that the graph is accurate, check the point of intersection\[\left( -1,4 \right)\]in both equations.
\[\begin{align}
& y=x+5 \\
& 4=-1+5 \\
& 4=4
\end{align}\]
\[\begin{align}
& y=-x+3 \\
& 4=-\left( -1 \right)+3 \\
& 4=1+3 \\
& 4=4
\end{align}\]
Coordinates of the point of intersection \[\left( -1,4 \right)\]and satisfy both the equations.
Hence, the graph of the system of equations is correct.
