In a corporate resource planning model, a team uses a system of linear equations to represent three different production constraints:

$\begin{cases} x - y + z = 2 \\ {}2x - y - z = -6 \\ {}2x + 2y + z = -3 \end{cases}$

A consultant suggests a resource profile represented by the ordered triple (-4, -3, 4). To verify this profile, you recall the definition of a solution to a system of equations. Which of the following statements correctly evaluates the consultant's proposal?

In a corporate resource planning model, a team uses the following system of linear equations to represent production constraints:

$\begin{cases} x - y + z = 2 \\ {}2x - y - z = -6 \\ {}2x + 2y + z = -3 \end{cases}$

True or False: The proposed resource plan $(-4, -3, 4)$ is officially classified as a solution to this system as long as it satisfies at least two out of the three equations.

In a corporate resource planning model where constraints are represented by a system of three linear equations, match each mathematical term with the definition that correctly describes its role in verifying a resource profile.

Verification Criteria for Resource Profiles

In a corporate resource planning model, a system of three equations represents weekly production constraints:

$\begin{cases} x - y + z = 2 \\ 2x - y - z = -6 \\ 2x + 2y + z = -3 \end{cases}$

An analyst is testing two proposed resource allocations: Profile A is $(-2, -1, 3)$ and Profile B is $(-4, -3, 4)$. Upon substituting the values into the system, the analyst finds that Profile A makes all three equations true. For Profile B, the first equation yields $-4 - (-3) + 4 = 3$, which is false because ${}3 \neq 2$. Recalling the fundamental rule for verifying solutions, the analyst concludes that the only valid solution to this system is Profile ____.