Determine if $(-2,-1,3)$ and $(-4,-3,4)$ are Solutions to a System of Three Equations

Determine if $(1,-3,2)$ and $(4,-1,-5)$ are Solutions to a System of Three Equations

A small business owner uses a system of three linear equations to manage constraints for the total cost, storage space, and delivery weight of three products. To verify if a proposed inventory count, represented by the ordered triple $(x, y, z)$, is a valid solution to this system, the owner substitutes the values into each equation. Which of the following conditions must be met for the inventory count to be considered a solution to the system?

A production manager is verifying a factory schedule using a system of three linear equations that represent constraints on labor, raw materials, and energy. If a proposed schedule, represented by the ordered triple $(x, y, z)$, results in a true statement for the labor and material equations but a false statement for the energy equation, the manager should record the schedule as a valid solution to the system.

A logistics coordinator manages warehouse space, shipping costs, and delivery times using a system of three linear equations. To verify if a proposed distribution plan (represented as the ordered triple $(x, y, z)$) is a valid solution, the values must produce a true statement for ____ of the equations in the system.

A facility manager must verify if a specific environmental configuration, represented by the ordered triple $(x, y, z)$, satisfies the safety requirements defined by a system of three linear equations (representing temperature, pressure, and humidity limits). Arrange the following steps in the correct order to determine if the configuration is a valid solution to the safety system.

A quality control technician is verifying if a set of three measurements, represented as the ordered triple $(x, y, z)$, satisfies a system of three linear equations representing safety standards. Match each component of the verification process with its correct definition.