Problem 52 - Introductory Algebra for College Students

Question

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. Solving an inconsistent system by substitution results in a true statement.

Step-by-Step Solution

Answer

The statement is false. The corrected statement is: 'Solving an inconsistent system by substitution results in a contradiction or an absurdity'.

Step 1: Understand the statement

The statement claims that if you solve an inconsistent system by substitution, you will end up with a true statement. This indicates that there would be a sensible answer. However, an inconsistent system should yield no solution or an absurdity such as '0 = 1'.

Step 2: Evaluate the statement

Since an inconsistent system doesn't yield a valid solution, and the statement suggests that it does, it's evident that the statement is false.

Step 3: Correct the statement

To correct the statement, you could say: 'Solving an inconsistent system by substitution results in a contradiction or an absurdity'.