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.