Question

Solve the system using substitution.

x+7y=0


2x−8y=22


(1 point)
Responses

(7, -1)
(7, -1)

(-7, -1)
(-7, -1)

(1, -7)
(1, -7)

(-1, -7)

Answer 1

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

1. \( x + 7y = 0 \) (Equation 1)
2. \( 2x - 8y = 22 \) (Equation 2)

First, let's solve Equation 1 for \( x \):

\[
x = -7y
\]

Now we can substitute \( x = -7y \) into Equation 2:

\[
2(-7y) - 8y = 22
\]

Simplifying this:

\[
-14y - 8y = 22
\]
\[
-22y = 22
\]

Now, divide both sides by -22:

\[
y = -1
\]

Now that we have \( y \), we can substitute it back into our expression for \( x \):

\[
x = -7(-1) = 7
\]

Thus, the solution to the system of equations is:

\[
(x, y) = (7, -1)
\]

The answer is \((7, -1)\).