To solve the system of equations:
- \( 3x + 7y = -11 \) (Equation 1)
- \( 5x + 7y = 5 \) (Equation 2)
We can start by eliminating one of the variables. We can subtract Equation 1 from Equation 2 to eliminate \( y \).
Step 1: Eliminate \( y \)
Subtract Equation 1 from Equation 2:
\[ (5x + 7y) - (3x + 7y) = 5 - (-11) \] This simplifies to:
\[ 5x - 3x = 5 + 11 \] \[ 2x = 16 \]
Step 2: Solve for \( x \)
Divide both sides by 2:
\[ x = 8 \]
Step 3: Substitute \( x \) back into one of the equations to find \( y \)
We can use Equation 1:
\[ 3(8) + 7y = -11 \] \[ 24 + 7y = -11 \]
Now, subtract 24 from both sides:
\[ 7y = -11 - 24 \] \[ 7y = -35 \]
Divide by 7:
\[ y = -5 \]
Final Solution:
The solution to the system of equations is:
\[ (x, y) = (8, -5) \]