Answer
See below:
Work Step by Step
In each equation in the system, find the intercepts.
Consider the first equation, \[2x-y=-1\]
\[y\text{-intercept}\]: Set x = 0
\[y=1\]
\[x\text{-intercept}\]: Set y = 0
\[x=-\frac{1}{2}\]
The line passes through \[\left( 0,1 \right)\] and \[\left( -\frac{1}{2},0 \right)\]
Now, consider the second equation \[x+y=-5\]
\[y\text{-intercept}\]: Set x = 0
\[y=-5\]
\[x\text{-intercept}\]: Set y = 0
\[x=-5\]
The line passes through \[\left( 0,-5 \right)\] and \[\left( -5,0 \right)\]
So, the intersection of both equations can be obtained by graphing them in the same plane as shown below:
So, Coordinates of the intersection point is \[\left( -2,-3 \right)\]
Now, check this point in both the equations,
Put \[\left( -2,-3 \right)\]in \[2x-y=-1\],
\[\begin{align}
& 2\left( -2 \right)-\left( -3 \right)=-1 \\
& -4+3=-1 \\
& -1=-1
\end{align}\]
Which is true.
Now, Put \[\left( -2,-3 \right)\]in \[x+y=-5\],
\[\begin{align}
& -2-3=-5 \\
& -5=-5
\end{align}\]
Which is true.
Hence, both the equations are verified.
Hence, solution of the system is \[\left\{ \left( -2,-3 \right) \right\}\].
