To solve this system of linear equations using substitution, we follow these steps:
Given:
[tex]\[
\begin{array}{l}
x = 3 + y \\
2x + 8y = -124
\end{array}
\][/tex]
1. Substitute the expression for [tex]\(x\)[/tex] from the first equation into the second equation.
The first equation gives us:
[tex]\[
x = 3 + y
\][/tex]
Substitute [tex]\(x\)[/tex] in the second equation:
[tex]\[
2(3 + y) + 8y = -124
\][/tex]
2. Simplify the equation
Distribute the 2 in the equation:
[tex]\[
6 + 2y + 8y = -124
\][/tex]
Combine like terms:
[tex]\[
6 + 10y = -124
\][/tex]
3. Isolate the variable [tex]\(y\)[/tex]
Subtract 6 from both sides of the equation:
[tex]\[
10y = -124 - 6
\][/tex]
Simplify the right-hand side:
[tex]\[
10y = -130
\][/tex]
Divide both sides by 10:
[tex]\[
y = \frac{-130}{10}
\][/tex]
[tex]\[
y = -13
\][/tex]
4. Substitute the value of [tex]\(y\)[/tex] back into the first equation to find [tex]\(x\)[/tex]
From the first equation, we had:
[tex]\[
x = 3 + y
\][/tex]
Substitute [tex]\(y = -13\)[/tex] into this equation:
[tex]\[
x = 3 + (-13)
\][/tex]
[tex]\[
x = 3 - 13
\][/tex]
[tex]\[
x = -10
\][/tex]
So, the solution to the system of equations is:
[tex]\[
(x, y) = (-10, -13)
\][/tex]
Thus, the correct answer is:
[tex]\[
\text{d. } (-10, -13)
\][/tex]
