Problem 50 - College Algebra Essentials

Question

Determine whether each statement makes sense or does not make sense, and explain your reasoning. I'm solving a three-variable system in which one of the given equations has a missing term, so it will not be necessary to use any of the original equations twice when I reduce the system to two equations in two variables.

Step-by-Step Solution

Answer

The statement does not make sense. Even if one equation has a missing term, you still have to use one of the equations twice in the process of reducing the system from three variables to two.

Step 1: Understanding System of Equations

To solve a system of equations, we often eliminate variables to simplify the problem. In a typical system of three equations with three variables, we need to use at least one equation twice in order to eliminate one variable completely.

Step 2: Considering the Missing Term

A missing term in one of the equations might make the process simpler. However, it does not change the fact that we need to use the same equation twice to eliminate one variable completely.

Step 3: Final Analysis

In evaluating the statement given, it is clear that the part of 'it will not be necessary to use any original equations twice even though one original equation has a missing term' does not make sense. Regardless of whether a term is missing in one of the equations, an equation will need to be used twice to reduce a three-variable system to a two-variable system.