To solve the system of equations using the substitution method, we start with the two equations:
- \( x = y - 4 \)
- \( x + 8y = 2 \)
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, combine like terms:
\[ y - 4 + 8y = 2 \] \[ 9y - 4 = 2 \]
To isolate \( y \), add 4 to both sides:
\[ 9y = 6 \]
Now, divide both sides by 9:
\[ y = \frac{6}{9} = \frac{2}{3} \]
Next, substitute \( y \) back into the first equation to find \( x \):
\[ x = \left( \frac{2}{3} \right) - 4 \] \[ x = \frac{2}{3} - \frac{12}{3} = -\frac{10}{3} \]
Now we have the solution:
\[ (x, y) = \left(-\frac{10}{3}, \frac{2}{3}\right) \]
Thus, the solution to the system of equations is:
\[ \left(-\frac{10}{3}, \frac{2}{3}\right) \]
Among the provided responses, it seems "left parenthesis negative 3 Start Fraction 1 over 3 End fraction comma Start Fraction 2 over 3 End fraction right parenthesis" corresponds to your solution as \(-\frac{10}{3}\) can be written as \(-3 \frac{1}{3}\).
Hence, the correct answer is:
\(\left(-3 \frac{1}{3}, \frac{2}{3}\right)\)
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