Question

solve the system by the substitution method.
x - 2y = -6
y = -4x + 12
select the correct choice below and, if necessary, fill in the answer box

Explanation:

Step1: Substitute \( y = -4x + 12 \) into \( x - 2y = -6 \)

Substitute \( y \) in the first equation: \( x - 2(-4x + 12) = -6 \)

Step2: Simplify and solve for \( x \)

Expand the equation: \( x + 8x - 24 = -6 \)
Combine like terms: \( 9x - 24 = -6 \)
Add 24 to both sides: \( 9x = 18 \)
Divide by 9: \( x = 2 \)

Step3: Substitute \( x = 2 \) into \( y = -4x + 12 \)

Calculate \( y \): \( y = -4(2) + 12 = -8 + 12 = 4 \)

Answer:

The solution to the system is \( x = 2 \), \( y = 4 \) (or as an ordered pair \((2, 4)\))