Question

Solve the system of equations below using elimination.

9x+3y=36


9x−5y=12


(1 point)
Responses

(2, 6)
(2, 6)

(3, 3)
(3, 3)

(−13, 3)
(−13, 3)

(-4, -24)

Answer 1

To solve the system of equations using elimination, let's write down the equations clearly:

1. \( 9x + 3y = 36 \) (Equation 1)
2. \( 9x - 5y = 12 \) (Equation 2)

First, we will eliminate \( x \). We can do this by manipulating the two equations. Notice that both equations have the term \( 9x \).

We can subtract Equation 1 from Equation 2:

\[
(9x - 5y) - (9x + 3y) = 12 - 36
\]

This simplifies to:

\[
-5y - 3y = -24
\]

Combining like terms gives:

\[
-8y = -24
\]

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

\[
y = \frac{-24}{-8} = 3
\]

Next, we will substitute \( y = 3 \) back into one of the original equations to find \( x \). We will use Equation 1:

\[
9x + 3(3) = 36
\]

This simplifies to:

\[
9x + 9 = 36
\]

Subtract 9 from both sides:

\[
9x = 36 - 9
\]

\[
9x = 27
\]

Now, divide by 9:

\[
x = \frac{27}{9} = 3
\]

So we have found that \( x = 3 \) and \( y = 3 \).

The solution to the system of equations is:

\[
(3, 3)
\]

Therefore, the response is **(3, 3)**.