To solve the system of equations
- \( 7x + 3y = -25 \) (Equation 1)
- \( -7x + 9y = -47 \) (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:
\[ \boxed{(-1, -6)} \]