To solve the system of equations:
- \( 7x + 3y = -25 \)
- \( -7x + 9y = -47 \)
we can use the method of elimination or substitution. Here, we will use elimination.
Step 1: Add the equations
If we add both equations together, the \( x \) terms will cancel out:
\[ (7x + 3y) + (-7x + 9y) = -25 + (-47) \]
This simplifies to:
\[ 0x + (3y + 9y) = -72 \]
\[ 12y = -72 \]
Step 2: Solve for \( y \)
Now, divide both sides by 12:
\[ y = \frac{-72}{12} = -6 \]
Step 3: Substitute \( y \) back into one of the original equations
Now that we have \( y \), we can substitute it back into one of the original equations to solve for \( x \). We can use the first equation:
\[ 7x + 3(-6) = -25 \]
\[ 7x - 18 = -25 \]
Step 4: Solve for \( x \)
Add 18 to both sides:
\[ 7x = -25 + 18 \]
\[ 7x = -7 \]
Now, divide both sides by 7:
\[ x = \frac{-7}{7} = -1 \]
Final Step: Write the solution
Thus, the solution to the system of equations is:
\[ (x, y) = (-1, -6) \]
Final answer: \((-1, -6)\)