If a given ordered triple solves the system of equations, is that solution unique? If so, explai

step 1 Hi, this is welcome to question 79. So in this question we asked that if order triple solves a s

If a given ordered triple solves the system of equations, is...

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Key Concepts

System of Equations

This concept involves multiple equations that share common variables. Each equation sets a condition, and a solution to the system is a set of values that satisfies every condition simultaneously. It is central in algebra and linear algebra when determining if a unique solution, infinitely many solutions, or no solution exists.

Unique versus Non-Unique Solutions

A unique solution means that there is exactly one set of variable values that satisfies all equations in the system. In contrast, a non-unique solution occurs when the equations are redundant or dependent, such that multiple or infinitely many ordered triples satisfy all conditions imposed by the system.

Consistency and Equation Dependency

Consistency refers to whether any solution exists for the system at all, while dependency addresses whether some equations are simply repetitions or linear combinations of others. When equations are dependent, they do not add new constraints, which can result in infinitely many solutions rather than a single unique solution.

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