Question

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

no solution
no solution

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

(23,−313)

Answer 1

To solve the system of equations using the substitution method, we'll start by substituting the expression for \( x \) from the first equation into the second equation.

The equations are:

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

Let's substitute \( x \) from equation 1 into equation 2:

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

Now, combine like terms:

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

\[
9y - 4 = 2
\]

Next, add 4 to both sides:

\[
9y = 6
\]

Now, divide both sides 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 \( x \):

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

To do this calculation, we'll convert 4 into a fraction:

\[
4 = \frac{12}{3}
\]

So,

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

Thus, the solution to the system is:

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

Since this does not match exactly with any of your given responses, make sure to check the formatting of your final answer closely with the available options.

However, looking at the options you presented, it appears that none of the responses represent the solution we found. Make sure to verify the original equations and try solving them once more if needed. If you need further clarification or have a different input set, please let me know!