To solve the system of equations using the substitution method, we have the following equations:
- \( x = y - 4 \)
- \( x + 8y = 2 \)
Let's substitute the expression for \( x \) from the first equation into the second equation.
Substituting \( x = y - 4 \) into the second equation:
\[ (y - 4) + 8y = 2 \]
Now, simplify this equation:
\[ y - 4 + 8y = 2 \] \[ 9y - 4 = 2 \]
Next, add 4 to both sides:
\[ 9y = 6 \]
Now, divide by 9 to solve for \( y \):
\[ y = \frac{6}{9} = \frac{2}{3} \]
Now that we have \( y \), we can find \( x \) using the first equation:
\[ x = y - 4 = \frac{2}{3} - 4 \] \[ x = \frac{2}{3} - \frac{12}{3} = \frac{2 - 12}{3} = \frac{-10}{3} \]
So the solution is:
\[ \left( \frac{-10}{3}, \frac{2}{3} \right) \]
This means that the correct response is:
\[ \left( -\frac{10}{3}, \frac{2}{3} \right) \]
However, when we compare this to the provided response options, \( \left( -3 \frac{1}{3}, \frac{2}{3} \right) \) appears to represent the same value as \( -\frac{10}{3} \), thus making the correct response as:
\[ \left( -3 \frac{1}{3}, \frac{2}{3} \right) \]
So, the correct answer is:
\((-3 \frac{1}{3}, \frac{2}{3})\).