Determine if the given ordered triple is a solution of the system. (4,1,2) {x-2 y =2 2

step 1 In this problem, we have a set of equations through three equations and three unknowns, X, Y, an

Determine if the given ordered triple is a solution of the...

Key Concepts

Systems of Linear Equations

A system of linear equations consists of multiple linear equations considered simultaneously. Each equation represents a plane (or line in two dimensions), and solving the system involves finding the point or points where all these planes intersect. This concept is fundamental in algebra and is used to determine values of variables that satisfy all equations at once.

Solution Verification

Solution verification involves checking whether a proposed solution satisfies every equation in the system. This is done by substituting the candidate values into each equation and ensuring that the left-hand side equals the right-hand side in every case. If all equations hold true, the candidate is indeed a solution to the system.

Substitution Method

The substitution method is a technique used for solving systems of equations by replacing a variable with an equivalent expression derived from another equation. This method simplifies the process by reducing the number of variables and making it easier to solve each equation step-by-step. Once a variable is isolated, its value is substituted back into other equations to find all variable values.

Ordered Triple

An ordered triple is a tuple consisting of three elements that typically represent the values of three variables in a system of equations. It provides a structured way to present solutions in three-dimensional space, where each component corresponds to a specific variable in the system. Checking an ordered triple as a solution means ensuring each component fits into its respective equation.

Transcript

Please give Ace some feedback