Answer
See below:
Work Step by Step
The provided system of equations is:
\[\begin{align}
& y=x+1 \\
& y=3x-1
\end{align}\]
To solve it by graph method, plot the two lines in rectangular coordinate system. Use the following steps:
Step 1:
First graph the line \[y=x+1\].
Find x-intercept, set \[y=0\] in above equation.
\[\begin{align}
& y=x+\grave{\ }1 \\
& 0=x+1 \\
& x=-1
\end{align}\]
Find y-intercept, set \[x=0\]in above equation.
\[\begin{align}
& y=x+1 \\
& y=0+1 \\
& y=1
\end{align}\]
Plot the ordered pairs \[\left( -1,0 \right)\text{ and }\left( 0,1 \right)\].
Step2:
Draw a line passes through \[\left( -1,0 \right)\]and \[\left( 0,1 \right)\].
Step3:
Now graph the line \[y=3x-1\].
Find x-intercept, set \[y=0\] in above equation.
\[\begin{align}
& y=3x-1 \\
& 0=3x-1 \\
& 3x=1 \\
& x=\frac{1}{3}
\end{align}\]
Find y-intercept, set \[x=0\]in above equation.
\[\begin{align}
& y=3x-1 \\
& y=3\cdot 0-1 \\
& y=-1
\end{align}\]
Plot the ordered pairs \[\left( \frac{1}{3},0 \right)\text{ and }\left( 0,-1 \right)\].
Step4:
Draw a line passes through \[\left( \frac{1}{3},0 \right)\]and \[\left( 0,-1 \right)\].
Step5:
From the graph, point of intersection is \[\left( 1,2 \right)\].
To ensure that the graph is accurate, check the point of intersection\[\left( 1,2 \right)\]in both equations.
\[\begin{align}
& y=x+1 \\
& 2=1+1 \\
& 2=2
\end{align}\]
\[\begin{align}
& y=3x-1 \\
& 2=3\cdot 1-1 \\
& 2=3-1 \\
& 2=2
\end{align}\]
Coordinates of the point of intersection \[\left( 1,2 \right)\]to satisfy both the equations.
Hence, the graph of the system of equations is correct.
