To solve the system of equations given by:
- \( y = -2x - 1 \)
- \( 3x - 4y = -51 \)
we can substitute the expression for \( y \) from the first equation into the second equation.
Step 1: Substitute \( y \) into the second equation
Substituting \( y = -2x - 1 \) into the second equation:
\[ 3x - 4(-2x - 1) = -51 \]
Step 2: Simplify the equation
Now, simplify the equation:
\[ 3x + 8x + 4 = -51 \] \[ 11x + 4 = -51 \]
Step 3: Solve for \( x \)
Now, subtract 4 from both sides:
\[ 11x = -51 - 4 \] \[ 11x = -55 \]
Now, divide by 11:
\[ x = -5 \]
Step 4: Solve for \( y \)
Now that we have \( x \), we can find \( y \) using the first equation \( y = -2x - 1 \):
\[ y = -2(-5) - 1 \] \[ y = 10 - 1 \] \[ y = 9 \]
Conclusion
The solution to the system of equations is:
\[ \boxed{(x, y) = (-5, 9)} \]