Question

1. a single-variable equation results from the elimination process and is solved to find the ____________ of the variable.
2. after obtaining a potential solution, it is important to ____________ the values into the original equations to ensure they truly solve the system.
3. the coefficients of the variable to be eliminated should ideally be ____________ but equal to use the elimination method without further manipulation.

Explanation:

1. When solving a single-variable equation from elimination, the goal is to find the specific value of that variable.
2. To confirm a solution works for the system, you substitute the found values back into the original equations to verify equality.
3. For the elimination method to work without extra steps, the coefficients of the variable to eliminate should be additive inverses (opposites), so they cancel when equations are combined.

Answer:

1. value
2. substitute
3. opposites (or negatives)