Question

Use the substitution method to solve the system x=y−4 , x+8y=2 .(1 point)
Responses

no solution
no solution

(23,−313)
left parenthesis Start Fraction 2 over 3 End Fraction comma negative 3 Start Fraction 1 over 3 End Fraction right parenthesis

(−313,23)
left parenthesis negative 3 Start Fraction 1 over 3 End Fraction comma Start Fraction 2 over 3 End Fraction right parenthesis

infinite solutions

Answer 1

To solve the system of equations using the substitution method, we have the equations:

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

First, we will substitute \( x \) from the first equation into the second equation.

Substituting \( x \) in equation 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 \( y \), we can substitute it back into the equation for \( x \):

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

Thus, the solution for the system of equations is:

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

Now, checking the options provided, the response \( ( -3 \frac{1}{3}, \frac{2}{3} ) \) is equivalent to \( \left( -\frac{10}{3}, \frac{2}{3} \right) \).

Thus, the correct answer is:

**Response: \((-3 \frac{1}{3}, \frac{2}{3})\)**.