Question

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

If a system has no solution, it is said to be inconsistent.

Short answer

The statement “If a system has no solution, it is said to be inconsistent.” 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.

When there is no solution for the given consistent system then it is said to be inconsistent system. The graphs of two equations are parallel to each other, that are why it not intersects at a point and there is no solution.

Therefore, the given statement is true.