Sure, let's proceed step-by-step to solve the given equation using the provided information and approach.
Step 1: Understand the given equation and substitution
The original equation is:
[tex]\[ -2x + y = -12 \][/tex]
We are given that [tex]\( y = -2 \)[/tex]. We need to substitute [tex]\( y = -2 \)[/tex] back into the equation.
Step 2: Substitute [tex]\( y = -2 \)[/tex] into the equation
Substitute [tex]\( y = -2 \)[/tex]:
[tex]\[ -2x + (-2) = -12 \][/tex]
Step 3: Simplify the equation
Simplify the equation by substituting the value of [tex]\( y \)[/tex]:
[tex]\[ -2x - 2 = -12 \][/tex]
Step 4: Summary based on substitution
We then rewrite the given part of the equation as:
[tex]\[ -2x - 2 = -12 \][/tex]
So, replacing the term for [tex]\( y \)[/tex] in the original equation, we get:
[tex]\[ -2x + \boxed{-2} = -12 \][/tex]
Now, as requested, the equation after substituting [tex]\( y = -2 \)[/tex] back is:
[tex]\[ -2x + \boxed{-2} = -12 \][/tex]
This completes the substitution process for this problem.
