Answer
See below:
Work Step by Step
System of equations
\[\begin{align}
& y=-x-1 \\
& 4x-3y=24
\end{align}\]
The provided system of equations is:
\[\begin{align}
& y=-x-1 \\
& 4x-3y=24
\end{align}\]
To solve it by graph method, plot two lines in rectangular coordinate system. Use the following steps:
Step 1:
First graph the line,\[y=-x-1\].
Find x-intercept, set \[y=0\] in above equation.
\[\begin{align}
& y=-x-1 \\
& 0=-x-1 \\
& x=-1
\end{align}\]
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 \[\left( -1,0 \right)\text{ and }\left( 0,-1 \right)\].
Step 2:
Draw a line passes through \[\left( -1,0 \right)\]and \[\left( 0,-1 \right)\].
Step 3:
Now graph the line \[4x-3y=24\].
Find x-intercept, set \[y=0\] in above equation.
\[\begin{align}
& 4x-3y=24 \\
& 4x-3\cdot 0=24 \\
& 4x=24 \\
& x=6
\end{align}\]
Find y-intercept, set \[x=0\]in above equation.
\[\begin{align}
& 4x-3y=24 \\
& 4\cdot 0-3y=24 \\
& -3y=24 \\
& y=-8
\end{align}\]
Plot the ordered pairs \[\left( 6,0 \right)\text{ and }\left( 0,-8 \right)\].
Step 4:
Draw a line passes through \[\left( 6,0 \right)\]and \[\left( 0,-8 \right)\].
Step 5:
From the graph, point of intersection is \[\left( 3,-4 \right)\].
To ensure that the graph is accurate, check the point of intersection\[\left( 3,-4 \right)\]in both equations.
\[\begin{align}
& y=-x-1 \\
& -4=-3-1 \\
& -4=-4
\end{align}\]
\[\begin{align}
& 4x-3y=24 \\
& 4\cdot 3-3\cdot \left( -4 \right)=24 \\
& 12+12=24 \\
& 24=24
\end{align}\]
Coordinates of the point of intersection \[\left( 3,-4 \right)\]satisfy both the equations.
Hence, the graph of the system of equations is correct.
