To solve the system of equations using the substitution method, we'll start with the two equations given:
- \( x = y - 4 \)
- \( x + 8y = 2 \)
Now, we can substitute the expression for \( x \) from the first equation into the second equation.
Substituting \( x \) in the second equation:
\[ (y - 4) + 8y = 2 \]
Now, simplify the equation:
\[ y - 4 + 8y = 2 \]
Combine like terms:
\[ 9y - 4 = 2 \]
Now, add 4 to both sides:
\[ 9y = 6 \]
Divide both sides by 9:
\[ y = \frac{6}{9} = \frac{2}{3} \]
Now, we can find \( x \) using the first equation \( x = y - 4 \):
\[ x = \frac{2}{3} - 4 \]
To subtract, it's helpful to convert 4 into a fraction:
\[ x = \frac{2}{3} - \frac{12}{3} = \frac{2 - 12}{3} = \frac{-10}{3} \]
So we have found:
\[ x = -\frac{10}{3}, \quad y = \frac{2}{3} \]
Thus the solution to the system of equations is:
\[ \left( -\frac{10}{3}, \frac{2}{3} \right) \]
Reviewing the provided answer choices:
- Negative 3 1/3, 2/3
- 2/3, -3 and 1/3
- Infinite solutions
- No solutions
The correct answer, matching our solution, is:
Negative 3 1/3, 2/3 (equivalently, \( -\frac{10}{3}, \frac{2}{3} \)).