Question

1. the system of equations below has a solution (x, y), which of the following is the value of x? x = -2y + 8 4x - 2y = 12

Explanation:

Step1: Substitute \( x = -2y + 8 \) into \( 4x - 2y = 12 \)

Substitute \( x \) in the second equation: \( 4(-2y + 8) - 2y = 12 \)

Step2: Expand and simplify the equation

Expand: \( -8y + 32 - 2y = 12 \)
Combine like terms: \( -10y + 32 = 12 \)
Subtract 32 from both sides: \( -10y = 12 - 32 = -20 \)
Divide by -10: \( y = \frac{-20}{-10} = 2 \)

Step3: Substitute \( y = 2 \) back into \( x = -2y + 8 \)

\( x = -2(2) + 8 = -4 + 8 = 4 \)

Answer:

\( 4 \)