To solve the system of equations using the substitution method, we start with the two equations:
- \( x = y - 4 \) (Equation 1)
- \( x + 8y = 2 \) (Equation 2)
We can substitute Equation 1 into Equation 2.
Substituting \( x = y - 4 \) into Equation 2:
\[ (y - 4) + 8y = 2 \]
Now, simplify the equation:
\[ y - 4 + 8y = 2 \] \[ 9y - 4 = 2 \]
Next, add 4 to both sides:
\[ 9y = 6 \]
Now, divide both sides by 9:
\[ y = \frac{2}{3} \]
Now that we have the value of \( y \), we can substitute it back into Equation 1 to find \( x \):
\[ x = y - 4 = \frac{2}{3} - 4 \]
To perform this subtraction, convert 4 to a fraction:
\[ x = \frac{2}{3} - \frac{12}{3} = \frac{2 - 12}{3} = \frac{-10}{3} \]
Thus, we have found:
- \( x = -\frac{10}{3} \)
- \( y = \frac{2}{3} \)
Therefore, the solution of the system, written in ordered pair format, is:
\[ \left( -\frac{10}{3}, \frac{2}{3} \right) \]
None of the provided response options match this solution. Let’s clarify if there was an oversight:
If the pairs provided were variations of \( (x, y) \) and were simplified incorrectly, please confirm if they were meant to be simplified or if you need further assistance finding matching pairs. Based on the calculations here, no conclusion can be drawn regarding infinite solutions or no solution given the nature of the equations provided.
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