You are a financial analyst determining the unit costs of three raw materials ($x$, $y$, and $z$) used in your company's manufacturing process. The cost relationships are modeled by the following system:

Eq 1: ${}3x - 4z = 0$ Eq 2: ${}3y + 2z = -3$ Eq 3: ${}2x + 3y = -5$

According to the elimination strategy to solve this specific system, after manipulating and combining Eq 1 and Eq 2 to successfully eliminate the shared variable $z$, what is the very next procedural step you must recall to progress toward the solution?

You are auditing a logistics model that uses a three-variable system to represent shipping constraints between three regional hubs. The relationships are defined by:

1. ${}3x - 4z = 0$
2. ${}3y + 2z = -3$
3. ${}2x + 3y = -5$

To solve this system using the elimination method described in your training manual, place the following procedural steps in the correct chronological order.

You are a production manager auditing the cost variances of three materials—$x$, $y$, and $z$—used in your factory. The variances are modeled by the following system of linear equations:

1. ${}3x - 4z = 0$
2. ${}3y + 2z = -3$
3. ${}2x + 3y = -5$

True or False: In the standard elimination procedure for this system, multiplying Equation 2 by 2 and adding it to Equation 1 successfully eliminates the variable $z$ and generates the two-variable equation ${}3x + 6y = -6$.

In your role as a production analyst, you are verifying the resource requirements for three components—$x$, $y$, and $z$—based on the following system of equations:

Eq 1: ${}3x - 4z = 0$ Eq 2: ${}3y + 2z = -3$ Eq 3: ${}2x + 3y = -5$

Match each procedural step of the elimination method with the specific mathematical outcome it produces as described in your training manual.

Logistics Resource Model: Final Variable Resolution

As a logistics analyst, you are auditing the solution steps for a resource optimization model based on the following system of equations:

1. ${}3x - 4z = 0$
2. ${}3y + 2z = -3$
3. ${}2x + 3y = -5$

According to the established elimination procedure, after the variable $z$ is removed, the resulting two-variable system is solved for $x$ by multiplying the equation ${}2x + 3y = -5$ by the constant ____.

Training Review: Logistics System Elimination Procedure