Question

solve the system by substitution.

$-5x + y = -50$

$y = -9x - 8$

Explanation:

Step1: Substitute \( y = -9x - 8 \) into \( -5x + y = -50 \)

Substitute \( y \) in the first equation with the expression from the second equation:
\( -5x + (-9x - 8) = -50 \)

Step2: Simplify and solve for \( x \)

Combine like terms:
\( -5x - 9x - 8 = -50 \)
\( -14x - 8 = -50 \)
Add 8 to both sides:
\( -14x = -50 + 8 \)
\( -14x = -42 \)
Divide both sides by -14:
\( x = \frac{-42}{-14} = 3 \)

Step3: Substitute \( x = 3 \) into \( y = -9x - 8 \) to find \( y \)

\( y = -9(3) - 8 \)
\( y = -27 - 8 \)
\( y = -35 \)

Answer:

The solution to the system is \( x = 3 \) and \( y = -35 \), or the ordered pair \( (3, -35) \).