Question

Use the substitution method to solve the system x = y – 4, x + 8y = 2

A. (-3 1/3, 2/3)
B. (2/3, -3 1/3)
C no solutions
D. Infinite solutions…

Answer 1

To solve the system of equations using the substitution method, we can start with the equations given:

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

Since the first equation gives us \( x \) in terms of \( y \), we can substitute \( x \) in the second equation:

Substituting \( x = y - 4 \) into the second equation:

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

Now, combine like terms:

\[
y - 4 + 8y = 2
\]
\[
9y - 4 = 2
\]

Next, add 4 to both sides:

\[
9y = 6
\]

Now, divide by 9:

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

Now that we have \( y \), we can substitute it back into the first equation to find \( x \):

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

So, the solution to the system of equations is:

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

In decimal form, the answer is approximately \((-3.33, 0.67)\).

Since this point is not in the provided options, let’s check the calculation once more.

From the original equations:

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

Which simplifies correctly as shown above leading to:

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

Now review the input options:

- A. \((-3 1/3, 2/3)\) corresponds to \(-\frac{10}{3}\) which translates to \(-3.33\) roughly, and this is the correct form.
- B. \((2/3, -3 1/3)\) does not match.
- C. no solutions do not match.
- D. Infinite solutions also do not match.

Thus the correct answer is:

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