To solve the system of equations using substitution, we first need to express one variable in terms of the other using one of the equations.
We have the two equations:
- \( 5x + y = -12 \) (Equation 1)
- \( 4x - y = 3 \) (Equation 2)
Let's solve Equation 1 for \( y \):
\[ y = -12 - 5x \]
Now we can substitute this expression for \( y \) into Equation 2:
\[ 4x - (-12 - 5x) = 3 \]
This simplifies to:
\[ 4x + 12 + 5x = 3 \]
Combine like terms:
\[ 9x + 12 = 3 \]
Now, isolate \( x \):
\[ 9x = 3 - 12 \] \[ 9x = -9 \] \[ x = -1 \]
Now that we have \( x \), we can substitute it back into the expression we found for \( y \):
\[ y = -12 - 5(-1) \] \[ y = -12 + 5 \] \[ y = -7 \]
Thus, the solution to the system of equations is:
\[ (x, y) = (-1, -7) \]
So your final answer is:
\[ (-1, -7) \]