Use the substitution method to solve the system x=y−4 , x+8y=2 .(1 point) Responses infinite solutions infinite solutions (−313,23) left parenthesis negative 3 Start Fraction 1 over 3 End Fraction comma Start Fraction 2 over 3 End Fraction right parenthesis no solution no solution (23,−313)

To solve the system of equations using the substitution method, let's first rewrite the given equations:

1. \( x = y - 4 \)
2. \( x + 8y = 2 \)

Now, we can substitute Equation 1 into Equation 2.

Substituting \( x = y - 4 \) into \( x + 8y = 2 \):

\[ (y - 4) + 8y = 2 \]

Now, simplify the equation:

\[ y - 4 + 8y = 2 \]

Combine like terms:

\[ 9y - 4 = 2 \]

Next, add 4 to both sides:

\[ 9y = 6 \]

Now, divide both sides by 9:

\[ y = \frac{6}{9} = \frac{2}{3} \]

Now that we have the value of \( y \), we can substitute it back into Equation 1 to find the value of \( x \):

\[ x = y - 4 \] \[ x = \frac{2}{3} - 4 \] \[ x = \frac{2}{3} - \frac{12}{3} = -\frac{10}{3} \]

So the solution to the system of equations is:

\[ \left(-\frac{10}{3}, \frac{2}{3}\right) \]

Now, looking at the choice of answers provided, it appears that none match this solution directly. However, using the approximate decimal equivalents for clarity:

• \( -\frac{10}{3} \) is approximately \( -3.33 \)
• \( \frac{2}{3} \) is approximately \( 0.67 \)

It seems none of the provided responses accurately represent the solution we found. Thus, based on the steps provided and the computations, the conclusion is that the answer does not accurately correspond to any options presented.

It could be noted that it might be an issue with the notation or approximation in the provided response options.