Answer
See below:
Work Step by Step
The provided system of equations is:
\[\begin{align}
& 2x-3y=6 \\
& 4x+3y=12
\end{align}\]
To solve it by graph method, plot the two lines in rectangular coordinate system. Use the following steps:
Step 1:
First graph the line \[2x-3y=6\].
Find x-intercept, set \[y=0\] in above equation.
\[\begin{align}
& 2x-3y=6 \\
& 2x-3\cdot 0=6 \\
& 2x=6 \\
& x=3
\end{align}\]
Find y-intercept, set \[x=0\]in above equation.
\[\begin{align}
& 2x-3y=6 \\
& 2\cdot 0-3y=6 \\
& -3y=6 \\
& y=-2
\end{align}\]
Plot the ordered pairs \[\left( 3,0 \right)\text{ and }\left( 0,-2 \right)\].
Step2:
Draw a line passing through \[\left( 3,0 \right)\]and \[\left( 0,-2 \right)\].
Step3:
Now graph the line \[4x+3y=12\].
Find x-intercept, set \[y=0\] in above equation.
\[\begin{align}
& 4x+3y=12 \\
& 4x+3\cdot 0=12 \\
& 4x=12 \\
& x=3
\end{align}\]
Find y-intercept, set \[x=0\]in above equation.
\[\begin{align}
& 4x+3y=12 \\
& 4\cdot 0+3y=12 \\
& 3y=12 \\
& y=4
\end{align}\]
Plot the ordered pairs \[\left( 3,0 \right)\text{ and }\left( 0,4 \right)\].
Step4:
Draw a line that passes through \[\left( 3,0 \right)\]and \[\left( 0,4 \right)\].
Step5:
From the graph, point of intersection is \[\left( 3,0 \right)\].
To ensure that the graph is accurate, check the point of intersection \[\left( 3,0 \right)\]in both equations.
\[\begin{align}
& 2x-3y=6 \\
& 2\cdot 3-3\cdot 0=6 \\
& 6-0=6 \\
& 6=6
\end{align}\]
\[\begin{align}
& 4x+3y=12 \\
& 4\cdot 3+3\cdot 0=12 \\
& 12+0=12 \\
& 12=12
\end{align}\]
Coordinates of the point of intersection \[\left( 3,0 \right)\] that satisfies both the equations.
Hence, the graph of the system of equations is correct.
