In Exercises 1–4, determine if the given ordered triple is a solution of the system. (2,−1, 3) x+ y+0z=4, x−2y−0z=1, 2x−y−2z=−1

Key Concepts

Ordered Triple

An ordered triple is a set of three numbers, typically represented as (x, y, z), which correspond to the variables in a three-dimensional space. In the context of systems of equations, an ordered triple is a potential solution that can satisfy multiple equations simultaneously. To verify if it is a solution, each value must be substituted into the equations to check for consistency.

System of Equations

A system of equations is a collection of two or more equations that share the same set of variables. The goal is to find values for these variables that satisfy all equations in the system simultaneously. In this case, the system consists of three linear equations, and the solution must satisfy each equation when the values of x, y, and z are substituted.

Substitution Method

The substitution method involves replacing variables in equations with their corresponding values to determine if a proposed solution is valid. For the given ordered triple (2, -1, 3), each variable is substituted into the equations of the system. If all equations hold true after substitution, the ordered triple is confirmed as a solution to the system.