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

Responses

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

no solution
no solution

infinite solutions
infinite solutions

(23,−313)

1 answer

To solve the system of equations using the substitution method, we first substitute the expression for \( x \) from the first equation into the second equation.

We have the following equations:

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

Now, we can substitute \( x \) in the second equation:

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

Now, we can simplify and solve for \( y \):

\[ y - 4 + 8y = 2 \] \[ 9y - 4 = 2 \] \[ 9y = 2 + 4 \] \[ 9y = 6 \] \[ y = \frac{6}{9} = \frac{2}{3} \]

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

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

Thus, the solution to the system of equations is:

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

So, the point is:

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

However, none of the provided responses exactly match with \(\left( -\frac{10}{3}, \frac{2}{3} \right)\). It seems like the right option is not included in your list.

Nonetheless, as per the calculations performed:

The solution to the system is: \[ \boxed{\left( -\frac{10}{3}, \frac{2}{3} \right)} \]