Question

he system by substitution.

$-5x - 9y = 33$

$-y - 1 = x$

Explanation:

Step1: Substitute \( x = -y - 1 \) into the first equation

We have the first equation \( -5x - 9y = 33 \) and \( x = -y - 1 \). Substitute \( x \) in the first equation:
\( -5(-y - 1) - 9y = 33 \)

Step2: Simplify the equation

Expand \( -5(-y - 1) \): \( 5y + 5 - 9y = 33 \)
Combine like terms: \( -4y + 5 = 33 \)
Subtract 5 from both sides: \( -4y = 33 - 5 = 28 \)

Step3: Solve for \( y \)

Divide both sides by -4: \( y = \frac{28}{-4} = -7 \)

Step4: Solve for \( x \)

Substitute \( y = -7 \) into \( x = -y - 1 \): \( x = -(-7) - 1 = 7 - 1 = 6 \)

Answer:

The solution to the system is \( x = 6 \), \( y = -7 \)