Question

Solve the system using substitution.

−7x+2y=18


6x+6y=0


(1 point)
Responses

(2, 2)
(2, 2)

(2, -2)
(2, -2)

(-2, -2)
(-2, -2)

(-2, 2)

Answer 1

To solve the system of equations using substitution, we need to solve one of the equations for one variable and then substitute that expression into the other equation.

The given system of equations is:

1. \( -7x + 2y = 18 \) (Equation 1)
2. \( 6x + 6y = 0 \) (Equation 2)

Let's solve Equation 2 for \(y\):

\[
6x + 6y = 0
\]

Divide the entire equation by 6:

\[
x + y = 0
\]

Now, solve for \(y\):

\[
y = -x
\]

Next, we substitute \(y = -x\) into Equation 1:

\[
-7x + 2(-x) = 18
\]

Simplifying the equation:

\[
-7x - 2x = 18
\]

Combining like terms:

\[
-9x = 18
\]

Now, solve for \(x\):

\[
x = -2
\]

Now that we have \(x\), we can substitute \(x = -2\) back into the expression for \(y\):

\[
y = -x = -(-2) = 2
\]

So the solution to the system of equations is:

\[
(x, y) = (-2, 2)
\]

Therefore, the correct response is:

**(-2, 2)**