To solve the system of equations using the substitution method, we have:
- \( x = y - 4 \)
- \( x + 8y = 2 \)
We will substitute the expression for \( x \) from the first equation into the second equation.
Step 1: Substitute \( x \) into the second equation.
Substituting \( x = y - 4 \) into \( x + 8y = 2 \):
\[ (y - 4) + 8y = 2 \]
Step 2: Simplify and solve for \( y \).
Combine like terms:
\[ y - 4 + 8y = 2 \ 9y - 4 = 2 \]
Now, add 4 to both sides:
\[ 9y = 2 + 4 \ 9y = 6 \]
Now, divide both sides by 9:
\[ y = \frac{6}{9} = \frac{2}{3} \]
Step 3: Substitute back to find \( x \).
Now that we have \( y \), we substitute it back into the first equation to find \( x \):
\[ x = y - 4 \ x = \frac{2}{3} - 4 \]
To subtract, convert 4 to a fraction:
\[ x = \frac{2}{3} - \frac{12}{3} = \frac{2 - 12}{3} = \frac{-10}{3} \]
Step 4: Write the solution.
Thus, the solution to the system is:
\[ (x, y) = \left( -\frac{10}{3}, \frac{2}{3} \right) \]
Looking at the response options provided, none of them match \( \left( -\frac{10}{3}, \frac{2}{3} \right) \).
It seems like the correct answer isn't listed in your provided options. Based on the calculations, you have:
The solution is:
\[ \boxed{\left( -\frac{10}{3}, \frac{2}{3} \right)} \]