To solve the system of equations using the substitution method, we'll start with the two equations you provided:
- \( x = y - 4 \) (Equation 1)
- \( x + 8y = 2 \) (Equation 2)
Step 1: Substitute Equation 1 into Equation 2
Let's substitute \( x \) from Equation 1 into Equation 2:
\[ (y - 4) + 8y = 2 \]
Step 2: Simplify the equation
Combine like terms:
\[ y - 4 + 8y = 2 \]
This simplifies to:
\[ 9y - 4 = 2 \]
Step 3: Solve for \( y \)
Add 4 to both sides:
\[ 9y = 6 \]
Now, divide by 9:
\[ y = \frac{6}{9} = \frac{2}{3} \]
Step 4: Substitute \( y \) back to find \( x \)
Now substitute \( y = \frac{2}{3} \) back into Equation 1 to find \( x \):
\[ x = \frac{2}{3} - 4 \]
Convert 4 to a fraction with the same denominator:
\[ x = \frac{2}{3} - \frac{12}{3} = \frac{2 - 12}{3} = \frac{-10}{3} \]
Step 5: Write the solution
Thus, the solution of the system is:
\[ \left( \frac{-10}{3}, \frac{2}{3} \right) \]
None of the provided responses match this solution directly. However, we can look at the nature of the solution to determine the appropriate response.
Since we found a unique solution, the answer from the given options is not included. But to address clarification:
- If \( \left(-\frac{10}{3}, \frac{2}{3}\right) \) was in the options, that would match our solution.
Given the responses you provided, there may be a misalignment with the expected solutions.
Final Result:
The solution is \( \left( -\frac{10}{3}, \frac{2}{3} \right) \).