Let's solve the system of equations step-by-step.
The given system of equations is:
[tex]\[
\begin{array}{l}
-5x = y - 5 \quad \text{(1)} \\
-2y = -x - 21 \quad \text{(2)}
\end{array}
\][/tex]
First, we'll solve Equation (1) for [tex]\( y \)[/tex]:
[tex]\[
-5x = y - 5
\][/tex]
[tex]\[
-5x + 5 = y
\][/tex]
[tex]\[
y = -5x + 5 \quad \text{(3)}
\][/tex]
Now, we substitute Equation (3) into Equation (2):
[tex]\[
-2(-5x + 5) = -x - 21
\][/tex]
Simplify inside the parentheses:
[tex]\[
-2(-5x) + (-2 \cdot 5) = -x - 21
\][/tex]
[tex]\[
10x - 10 = -x - 21
\][/tex]
Next, combine like terms:
[tex]\[
10x + x = -21 + 10
\][/tex]
[tex]\[
11x = -11
\][/tex]
[tex]\[
x = -1 \quad \text{(4)}
\][/tex]
Now that we have [tex]\( x \)[/tex], substitute [tex]\( x = -1 \)[/tex] back into Equation (3) to solve for [tex]\( y \)[/tex]:
[tex]\[
y = -5(-1) + 5
\][/tex]
[tex]\[
y = 5 + 5
\][/tex]
[tex]\[
y = 10 \quad \text{(5)}
\][/tex]
Therefore, the solution to the system of equations is:
[tex]\[
(x, y) = (-1, 10)
\][/tex]
So, the correct answer is:
A. [tex]\((-1, 10)\)[/tex]
