Question

u3 solve the system by the method of your choice.
y = 3x - 8
-2x - 3y = 2
x = \boxed{ } \quad y = \boxed{ }

Explanation:

Step1: Substitute \( y = 3x - 8 \) into \( -2x - 3y = 2 \)

Substitute \( y \) in the second equation: \( -2x - 3(3x - 8) = 2 \)

Step2: Simplify the equation

Expand and simplify: \( -2x - 9x + 24 = 2 \)
Combine like terms: \( -11x + 24 = 2 \)
Subtract 24 from both sides: \( -11x = 2 - 24 = -22 \)
Divide by -11: \( x = \frac{-22}{-11} = 2 \)

Step3: Find \( y \) using \( y = 3x - 8 \)

Substitute \( x = 2 \): \( y = 3(2) - 8 = 6 - 8 = -2 \)

Answer:

\( x = 2 \), \( y = -2 \)