To solve the given system of equations using substitution, follow these steps:
1. Identify the two equations:
[tex]\[
\begin{aligned}
x - 6y &= 56 \quad \text{(Equation 1)} \\
5y - 6x &= -26 \quad \text{(Equation 2)}
\end{aligned}
\][/tex]
2. Solve Equation 1 for [tex]\(x\)[/tex]:
[tex]\[
x - 6y = 56
\][/tex]
Add [tex]\(6y\)[/tex] to both sides to isolate [tex]\(x\)[/tex]:
[tex]\[
x = 56 + 6y
\][/tex]
3. Substitute [tex]\(x = 56 + 6y\)[/tex] into Equation 2:
[tex]\[
5y - 6(56 + 6y) = -26
\][/tex]
4. Simplify and solve for [tex]\(y\)[/tex]:
[tex]\[
5y - 336 - 36y = -26
\][/tex]
Combine like terms:
[tex]\[
-31y - 336 = -26
\][/tex]
Add 336 to both sides:
[tex]\[
-31y = 310
\][/tex]
Divide by -31:
[tex]\[
y = \frac{310}{-31}
\][/tex]
[tex]\[
y = -10
\][/tex]
5. Substitute [tex]\(y = -10\)[/tex] back into the expression [tex]\(x = 56 + 6y\)[/tex]:
[tex]\[
x = 56 + 6(-10)
\][/tex]
[tex]\[
x = 56 - 60
\][/tex]
[tex]\[
x = -4
\][/tex]
6. Write the solution as an ordered pair:
[tex]\[
(x, y) = (-4, -10)
\][/tex]
So, the solution set is [tex]\((-4, -10)\)[/tex].
The correct answer is:
A. The solution set is [tex]\(\boxed{(-4, -10)}\)[/tex].
