Question

State whether each sentence is true or false. If false, replace the underlined term to make a true sentence.

If a system has at least one solution, it is said to be consistent.

Short answer

The statement “If a system has at least one solution, it is said to be consistent.” istrue.

Step-by-step solution

Step 1. State the concept of consistent and inconsistent solution.

A system of two linear equations can have one solution, an infinite number of solutions, or no solution.

1. If a system has at exactly one solution, more than one solution or infinitely many solutions, then it is said to be consistent.
2. If a system of equations has no solution, then it is said to be inconsistent.

Step 2. Explanation of the statement.

Since, a system of two linear equations can have the following three solution conditions:

• One solution
• An infinite number of solutions
• No solution.

That’s why the systems of equations are classified by the set of solutions to satisfy the equations.

Step 3. State the conclusion.

If the system of two equations contains at least one solution it is said to be consistent. Hence, the given statement is true.