Question

State whether the following statement is true or false. If false, tell why. If the elimination method leads to 0 = -2, the solution set of the system is {(0, -2)}.

A. True

B. False, the solution set is Ø.

C. False, the equations are equivalent and the solution set is one of the equations.

D. False, the solution set is {(-2,0)}.

Answer 1

Answer: B. False, the solution set is Ø.

Step-by-step explanation:

If the elimination method leads to 0 = -2, then that's a false statement. This then has a chain reaction to cause the original system to be inconsistent, meaning there aren't any solutions.

We consider the solution set to be the empty set, denoted with the special symbol of Ø which unfortunately looks like the number 0, but they're different symbols.

Perhaps better notation is to write a pair of curly braces with nothing inside them. So you'd write { } to indicate the empty set.