Question

Use the elimination method to solve the follow system of equations.

9x - 7y = 22

x + 3y = -24

A 3,-9
B 0, -8
C -3, -7
D 4,2

Answer 1

To solve the system of equations using the elimination method, we have:

1. \( 9x - 7y = 22 \) (Equation 1)
2. \( x + 3y = -24 \) (Equation 2)

First, we will manipulate Equation 2 so that it can be easily eliminated with Equation 1. We can multiply Equation 2 by 9 to match the coefficient of \( x \) in Equation 1:

\[
9(x + 3y) = 9(-24)
\]

This gives us:

\[
9x + 27y = -216 \quad (Equation 3)
\]

Now we have a new equation (Equation 3) and will write the system again:

1. \( 9x - 7y = 22 \) (Equation 1)
3. \( 9x + 27y = -216 \) (Equation 3)

Next, we'll subtract Equation 1 from Equation 3 to eliminate \( x \):

\[
(9x + 27y) - (9x - 7y) = -216 - 22
\]

This simplifies to:

\[
27y + 7y = -238
\]

\[
34y = -238
\]

Now, solve for \( y \):

\[
y = \frac{-238}{34} = -7
\]

Next, we substitute \( y = -7 \) back into Equation 2 to solve for \( x \):

\[
x + 3(-7) = -24
\]

\[
x - 21 = -24
\]

Adding 21 to both sides gives us:

\[
x = -3
\]

So, we have \( x = -3 \) and \( y = -7 \). The solution is:

\[
(x, y) = (-3, -7)
\]

Looking at the answer choices:

A) (3, -9)
B) (0, -8)
C) (-3, -7)
D) (4, 2)

The correct answer is **C) (-3, -7)**.