Question

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

no solution
no solution

infinite solutions


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

(−3 1/3,2/3)

Answer 1

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:

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

**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)**