Consider the system of equations shown.
[tex]\[
\begin{cases}
y = x + 11 \\
-y = -x + 11
\end{cases}
\][/tex]

What is the solution to this system of equations?

A. [tex]\((0, 11)\)[/tex]

B. [tex]\((0, -11)\)[/tex]

C. No solution

D. Infinitely many solutions



Answer :

Let's analyze the given system of equations step-by-step to determine if there is a solution.

The system of equations is:
[tex]\[ \left\{ \begin{array}{l} y = x + 11 \\ -y = -x + 11 \end{array} \right. \][/tex]

First, let's simplify the second equation:
[tex]\[ -y = -x + 11 \][/tex]
Multiply both sides of this equation by [tex]\(-1\)[/tex] to make [tex]\(y\)[/tex] the subject:
[tex]\[ y = x - 11 \][/tex]

Now the system of equations looks like this:
[tex]\[ \left\{ \begin{array}{l} y = x + 11 \\ y = x - 11 \end{array} \right. \][/tex]

Next, we will set the right-hand sides of these two equations equal to each other, because both are equal to [tex]\(y\)[/tex]:
[tex]\[ x + 11 = x - 11 \][/tex]

Subtract [tex]\(x\)[/tex] from both sides of the equation:
[tex]\[ 11 = -11 \][/tex]

This results in a contradiction. The statement [tex]\(11 = -11\)[/tex] is never true, which means that there is no value of [tex]\(x\)[/tex] that satisfies both equations simultaneously.

Therefore, the system of equations has no solution.

In conclusion, the answer is:
[tex]\[ \boxed{\text{no solution}} \][/tex]