Question

Solve the system of equations.
7x+3y=−25

−7x+9y=−47
(1 point)
(
,
)

Answer 1

To solve the system of equations

1. \( 7x + 3y = -25 \) (Equation 1)
2. \( -7x + 9y = -47 \) (Equation 2)

we can use the method of elimination or substitution. Here, I'll use the elimination method.

First, let's add both equations to eliminate \(x\):

\[
(7x + 3y) + (-7x + 9y) = -25 + (-47)
\]

Simplifying, we get:

\[
0 + 12y = -72
\]

Now, solve for \(y\):

\[
12y = -72
\]
\[
y = \frac{-72}{12} = -6
\]

Now that we have \(y\), we can substitute \(y = -6\) back into one of the original equations to find \(x\). We'll use Equation 1:

\[
7x + 3(-6) = -25
\]
\[
7x - 18 = -25
\]
\[
7x = -25 + 18
\]
\[
7x = -7
\]
\[
x = \frac{-7}{7} = -1
\]

Thus, the solution to the system of equations is:

\[
(x, y) = (-1, -6)
\]

So, the final answer is:

\[
\boxed{(-1, -6)}
\]