To solve the system of equations:
- \( 7x + 3y = -25 \) (Equation 1)
- \( -7x + 9y = -47 \) (Equation 2)
We can use either the substitution method or the elimination method. Here, we'll use the elimination method.
First, we can add Equation 1 and Equation 2 together to eliminate \( x \):
\[ (7x + 3y) + (-7x + 9y) = -25 - 47 \]
This simplifies to:
\[ 0 + 12y = -72 \]
Now we can solve for \( y \):
\[ 12y = -72 \] \[ y = \frac{-72}{12} = -6 \]
Now that we have \( y \), we can substitute \( y = -6 \) back into Equation 1 to find \( x \):
\[ 7x + 3(-6) = -25 \] \[ 7x - 18 = -25 \] \[ 7x = -25 + 18 \] \[ 7x = -7 \] \[ x = \frac{-7}{7} = -1 \]
So, the solution to the system of equations is:
\[ x = -1, \quad y = -6 \]
Thus, the solution is \( (x, y) = (-1, -6) \).