A logistics analyst is using determinant methods to solve a system of linear equations representing route capacities. Match each set of calculated determinant results with the correct description of the system's solutions.

A budget analyst is using a software tool to solve a system of linear equations representing department expenses. The tool reports that the main coefficient determinant $D$ is exactly 0. Which of the following conditions correctly identifies that the system is inconsistent (has no solution)?

A supply chain analyst is using determinants to solve a system of equations representing inventory levels. If the analyst finds that the main coefficient determinant $D$ is equal to zero and all variable determinants (such as $D_x$, $D_y$, and $D_z$) are also exactly zero, the system is classified as inconsistent.

Classifying Systems in Resource Allocation

An inventory planner is using Cramer's rule to analyze a system of linear equations that models warehouse storage capacities. They calculate the main coefficient determinant and find that $D = 0$. They also calculate the variable determinants and find that $D_x = 0$, $D_y = 0$, and $D_z = 0$. This tells the planner that the system of equations is __________, which means there are infinitely many valid storage configurations.

Material Cost Model Determinant Analysis

A scheduling analyst at a shipping hub is using Cramer's rule to analyze a system of linear equations representing truck route constraints. The analyst needs to determine if the system is dependent (infinitely many valid schedules) or inconsistent (no possible schedules).

Arrange the steps in the correct order to classify the system, starting from the very first calculation.