Question

y=-2x-1
3x-4y=-51

Answer 1

To solve the system of equations given by:

1. \( y = -2x - 1 \)
2. \( 3x - 4y = -51 \)

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:

\[
\boxed{(x, y) = (-5, 9)}
\]