To solve the system of equations using the substitution method, we need to substitute the expression for \( x \) from the first equation into the second equation.
The system of equations is:
- \( x = y - 4 \)
- \( x + 8y = 2 \)
Step 1: Substitute the first equation into the second equation.
Substituting \( x \) in the second equation:
\[ (y - 4) + 8y = 2 \]
Step 2: Combine like terms.
\[ y - 4 + 8y = 2 \]
\[ 9y - 4 = 2 \]
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 into the first equation to solve for \( x \).
Using \( y = \frac{2}{3} \):
\[ x = y - 4 \]
\[ x = \frac{2}{3} - 4 \]
Convert 4 to a fraction with a denominator of 3:
\[ x = \frac{2}{3} - \frac{12}{3} = \frac{2 - 12}{3} = \frac{-10}{3} \]
Step 5: Write the solution as an ordered pair.
The solution to the system of equations is:
\[ \left( \frac{-10}{3}, \frac{2}{3} \right) \]
However, looking at the provided responses, it appears that the point \((−3 \frac{1}{3}, 2/3)\) can be expressed as \((- \frac{10}{3}, \frac{2}{3})\).
Thus, the answer is:
(−3 1/3, 2/3)
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