Answer
See below:
Work Step by Step
The provided system of equations is:
\[\begin{align}
& 4x+y=4 \\
& 3x-y=3
\end{align}\]
To solve it by graph method, plot two lines in rectangular coordinate system. Use the following steps:
Step 1:
First graph the line \[4x+y=4\].
Find x-intercept, set \[y=0\] in above equation.
\[\begin{align}
& 4x+y=4 \\
& 4x+0=4 \\
& x=1
\end{align}\]
Find y-intercept, set \[x=0\]in above equation.
\[\begin{align}
& 4x+y=4 \\
& 4\cdot 0+y=4 \\
& y=4
\end{align}\]
Plot the ordered pairs \[\left( 1,0 \right)\text{ and }\left( 0,4 \right)\].
Step 2:
Draw a line passing through \[\left( 1,0 \right)\]and \[\left( 0,4 \right)\].
Step 3:
Now graph the line \[3x-y=3\].
Find x-intercept, set \[y=0\] in above equation.
\[\begin{align}
& 3x-y=3 \\
& 3x-0=3 \\
& x=1
\end{align}\]
Find y-intercept, set \[x=0\]in above equation.
\[\begin{align}
& 3x-y=3 \\
& 3\cdot 0-y=3 \\
& y=-3
\end{align}\]
Plot the ordered pairs \[\left( 1,0 \right)\text{ and }\left( 0,-3 \right)\].
Step 4:
Draw a line passing through \[\left( 1,0 \right)\]and \[\left( 0,-3 \right)\].
Step 5:
From the graph, point of intersection is \[\left( 1,0 \right)\].
To ensure that the graph is accurate, check the point of intersection\[\left( 1,0 \right)\]in both equations.
\[\begin{align}
& 4x+y=4 \\
& 4\cdot 1+0=4 \\
& 4+0=4 \\
& 4=4
\end{align}\]
\[\begin{align}
& 3x-y=3 \\
& 3\cdot 1-0=3 \\
& 3-0=3 \\
& 3=3
\end{align}\]
Coordinates of the point of intersection \[\left( 1,0 \right)\]and satisfy both the equations.
Hence, the graph of the system of equations is correct.
