Question

Use the substitution method to solve the system x equals y minus 4, x + 8y = 2
Negative 3 1/3, 2/3
2/3, -3 and 1/3
Infinite solutions
No solutions

Answer 1

To solve the system of equations using the substitution method, we'll start with the two equations given:

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

Now, we can substitute the expression for \( x \) from the first equation into the second equation.

Substituting \( x \) in the second equation:

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

Now, simplify the equation:

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

Combine like terms:

\[
9y - 4 = 2
\]

Now, add 4 to both sides:

\[
9y = 6
\]

Divide both sides by 9:

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

Now, we can find \( x \) using the first equation \( x = y - 4 \):

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

To subtract, it's helpful to convert 4 into a fraction:

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

So we have found:

\[
x = -\frac{10}{3}, \quad y = \frac{2}{3}
\]

Thus the solution to the system of equations is:

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

Reviewing the provided answer choices:

- Negative 3 1/3, 2/3
- 2/3, -3 and 1/3
- Infinite solutions
- No solutions

The correct answer, matching our solution, is:

**Negative 3 1/3, 2/3** (equivalently, \( -\frac{10}{3}, \frac{2}{3} \)).