Question

Solve the system of equations below using substitution.

x=2y+6


x=5y−12


(1 point)
Responses

(18, 6)
(18, 6)

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

(-6, -6)
(-6, -6)

(10, 2)

Answer 1

To solve the system of equations using substitution, we have the following equations:

1. \( x = 2y + 6 \)
2. \( x = 5y - 12 \)

Since both equations are equal to \( x \), we can set them equal to each other:

\[
2y + 6 = 5y - 12
\]

Now, rearranging the equation to solve for \( y \):

\[
6 + 12 = 5y - 2y
\]

\[
18 = 3y
\]

\[
y = 6
\]

Now that we have found \( y \), we can substitute it back into one of the original equations to find \( x \). We'll use the first equation:

\[
x = 2y + 6
\]

Substituting \( y = 6 \):

\[
x = 2(6) + 6 = 12 + 6 = 18
\]

So, we have:

\[
x = 18, \quad y = 6
\]

The solution to the system of equations is \( (18, 6) \).

Thus, the correct response is:

(18, 6)