A logistics coordinator is using the ordered triple $(1, -3, 2)$ as a test case for a routing system. To verify if this triple satisfies the first equation of the system, ${}3x + y + z = 2$, which of the following represents the correct substitution of the triple's values into the left side of the equation?

An inventory manager is evaluating a 'net change' proposal represented by the ordered triple $(1, -3, 2)$, where each value represents a unit adjustment in one of three storage zones. To verify that this triple is a solution to the following system of balance equations, arrange the verification steps in the correct logical order:

$\left\{\begin{array}{l} 3x + y + z = 2 \\ x + 2y + z = -3 \\ 3x + y + 2z = 4 \end{array}\right.$

An operations analyst is verifying whether the ordered triple $(1, -3, 2)$ is a solution for the following system of efficiency constraints:

• ${}3x + y + z = 2$
• $x + 2y + z = -3$
• ${}3x + y + 2z = 4$

Match each variable or property with its corresponding value or status based on the data provided in this test case.

A technical auditor is reviewing a set of system constraints defined by the following equations:

• ${}3x + y + z = 2$
• $x + 2y + z = -3$
• ${}3x + y + 2z = 4$

True or False: The ordered triple $(1, -3, 2)$ is a valid solution to this system because it satisfies all three equations when $x = 1$, $y = -3$, and $z = 2$ are substituted.

A project manager is reviewing a resource allocation model consisting of a system of three linear equations. To verify that the ordered triple $(1, -3, 2)$ is a solution to this system, the manager substitutes $x = 1$, $y = -3$, and $z = 2$ into each equation. The manager concludes the triple is a comprehensive solution because the substitution results in a ____ arithmetic statement for all three equations.