An office manager is using a system of two linear equations to compare the hourly rates of two different staffing agencies. To solve this system using Cramer's Rule, arrange the following steps in the correct procedural order.

A catering manager at 'Elite Events' is solving for the number of vegetarian meals ($x$) and chicken meals ($y$) to prepare for a banquet. The constraints for preparation time and kitchen capacity lead to the following system of equations:

${}2x + 5y = 150$ ${}3x + 4y = 170$

Match each component of Cramer's Rule to its correct mathematical setup for this specific system.

A logistics coordinator is using a system of two linear equations to determine the optimal number of shipments for two different routes ($x$ and $y$). After setting up the system, the coordinator calculates the determinant of the coefficient matrix ($D$) and the determinant created by replacing the $x$-column with the constant terms ($D_x$). According to Cramer’s Rule, which formula should be used to find the value of $x$?

Constructing the Determinant $D_y$ in Cramer's Rule

A resource analyst is using Cramer's Rule to solve for two variables, $x$ and $y$, to optimize production levels. The main determinant, $D$, is evaluated using the constant terms from the right side of the system's equations.

A project manager is using Cramer's Rule to solve a system of two linear equations to determine the hourly rates of two contractors. To set up the main determinant ($D$) for this calculation, the manager must use the ____ of the variables from the equations.