Let's match each term on the left with its correct definition on the right. I'll go through them step-by-step: --- ### 1. Inconsistent equations **Definition:** A collection of equations with no solution. --- ### 2. Solution Set **Definition:** The collection of all lists \((x_1, x_2, \ldots, x_n)\) which make each equation true. --- ### 3. Equivalent linear systems **Definition:** Collections of equations which have the same solution set. --- ### 4. Elementary Row Operations **Definition:** Replacement, Interchange, Scaling. --- ### 5. Solution **Definition:** A list of numbers that makes each equation true. --- ### 6. Consistent equations **Definition:** A collection of equations which have at least one solution. --- ### 7. Linear equation **Definition:** \(a_1x_1 + a_2x_2 + \cdots + a_nx_n = b\) --- ## Final Answers (in order): 1. Inconsistent equations — A collection of equations with no solution. 2. Solution Set — The collection of all lists \((x_1, x_2, \ldots, x_n)\) which make each equation true. 3. Equivalent linear systems — Collections of equations which have the same solution set. 4. Elementary Row Operations — Replacement, Interchange, Scaling. 5. Solution — A list of numbers that makes each equation true. 6. Consistent equations — A collection of equations which have at least one solution. 7. Linear equation — \(a_1x_1 + a_2x_2 + \cdots + a_nx_n = b\) --- **Explanation:** Each term describes a specific property or component of systems of linear equations. The definitions clarify the concepts, matching the terminology used in linear algebra.