Solve the system of equations by graphing:
\[
\left\{\begin{array}{l}
y=-x-1 \\
y=2 x+11
\end{array}\right.
\]

First graph each line, then place a dot indicating the solution to the system.
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Step 1 ：Graph the first equation, \(y = -x - 1\). This is a straight line with a slope of -1 and a y-intercept of -1.

Step 2 ：Graph the second equation, \(y = 2x + 11\). This is a straight line with a slope of 2 and a y-intercept of 11.

Step 3 ：The solution to the system of equations is the point where the two lines intersect. To find this point, we set the two equations equal to each other and solve for x: \(- x - 1 = 2x + 11\).

Step 4 ：Combine like terms: \(-3x = 12\).

Step 5 ：Divide by -3: \(x = -4\).

Step 6 ：Substitute \(x = -4\) into the first equation to find y: \(y = -(-4) - 1 = 4 - 1 = 3\).

Step 7 ：So, the solution to the system of equations is the point \((-4, 3)\). This is the point where the two lines intersect on the graph.

Step 8 ：To check the solution, substitute \(x = -4\) and \(y = 3\) into both original equations. If both equations are true, then the solution is correct.

Step 9 ：For the first equation: \(y = -x - 1\), \(3 = -(-4) - 1\), \(3 = 4 - 1\), \(3 = 3\).

Step 10 ：For the second equation: \(y = 2x + 11\), \(3 = 2(-4) + 11\), \(3 = -8 + 11\), \(3 = 3\).

Step 11 ：Since both equations are true, the solution is correct. The point \((-4, 3)\) is the solution to the system of equations. The final answer is \(\boxed{(-4, 3)}\).