To solve the given system of equations using the substitution method, we have:
- \( x = y - 4 \) (equation 1)
- \( x + 8y = 2 \) (equation 2)
First, we will substitute equation 1 into equation 2:
Substituting \( x \) in equation 2: \[ (y - 4) + 8y = 2 \]
Combine like terms: \[ y - 4 + 8y = 2 \implies 9y - 4 = 2 \]
Now, add 4 to both sides: \[ 9y = 6 \]
Now, divide by 9: \[ y = \frac{6}{9} = \frac{2}{3} \]
Next, we will substitute the value of \( y \) back into equation 1 to find \( x \): \[ x = y - 4 = \frac{2}{3} - 4 \]
Convert 4 to a fraction with the same denominator: \[ 4 = \frac{12}{3} \]
So, we have: \[ x = \frac{2}{3} - \frac{12}{3} = \frac{2 - 12}{3} = \frac{-10}{3} \]
Thus, the solution to the system is: \[ \left( -\frac{10}{3}, \frac{2}{3} \right) \]
Based on the options provided, the correct choice corresponding to the values we found is: \[ \left( -\frac{10}{3}, \frac{2}{3} \right) \]