To solve the given system of equations:
[tex]\[
\left\{
\begin{array}{c}
y = x + 11 \\
-y = -x + 11
\end{array}
\right.
\][/tex]
Let's simplify the second equation to make it more comparable to the first. Simplifying [tex]\(-y = -x + 11\)[/tex] results in:
[tex]\[
y = x - 11
\][/tex]
Now we have the following system of equations:
[tex]\[
\left\{
\begin{array}{c}
y = x + 11 \\
y = x - 11
\end{array}
\right.
\][/tex]
To find the solution, we set the right-hand sides of the equations equal to each other:
[tex]\[
x + 11 = x - 11
\][/tex]
Subtracting [tex]\(x\)[/tex] from both sides, we get:
[tex]\[
11 = -11
\][/tex]
This statement is a contradiction and is never true. This means there is no value of [tex]\(x\)[/tex] that can satisfy both equations simultaneously.
Therefore, there is no solution to this system of equations. The correct answer is:
no solution
