Learn Before
Determining Whether an Ordered Triple is a Solution:
To evaluate whether the ordered triple represents a solution to the system of linear equations \left\{\begin{array}{l} x - y + z = 2 \ 2x - y - z = -6 \ 2x + 2y + z = -3 \end{array} ight., substitute the values , , and into each equation. Testing the first equation yields . Because does not equal , the substitution results in a strictly false mathematical statement. Since an ordered triple must successfully satisfy all equations in the system simultaneously, the failure of the first equation definitively proves that is not a solution.
0
1
Tags
OpenStax
Intermediate Algebra @ OpenStax
Ch.4 Systems of Linear Equations - Intermediate Algebra @ OpenStax
Algebra
Related
Determining Whether an Ordered Pair is a Solution of a System of Equations
Solving a System of Linear Equations by Graphing
Solving by Graphing
Solving by Substitution
A project manager is comparing two different service contracts using a system of linear equations. In this context, what is the definition of a solution to this system?
A project manager is evaluating two different vendor bids by comparing their cost formulas. For a specific set of values to be a solution to this system of equations, those values must make every equation in the system true.
Defining Solutions in a Business System
In a professional setting, mathematical models are often used to compare different financial scenarios or vendor costs. Match each term below to the definition that best describes its role in a system of equations.
In a professional analysis comparing two different vendor pricing models using a system of linear equations, an ordered pair is defined as a solution only if it makes ________ of the equations in the system true simultaneously.
Vendor Cost Verification
A production supervisor is verifying if a specific staffing allocation is a 'solution' to a system of equations representing two different department budget constraints. Arrange the logical steps in the correct order to recall the process of identifying a valid solution for the entire system.
Defining a Solution in Professional Cost Modeling
An operations manager is using a coordinate graph to compare two different utility service plans, each represented by a linear equation. To identify the 'solution' to this system of equations on the graph, which feature should the manager locate?
A resource planner is evaluating whether a specific coordinate is a 'solution' to a system of two budget equations. If the coordinate satisfies the first budget equation but makes the second budget equation false, which of the following statements is true based on the definition of a solution to a system?
System of Three Linear Equations with Three Variables
Determining Whether an Ordered Triple is a Solution to a System of Three Linear Equations
Determining Whether an Ordered Triple is a Solution:
Determining Whether an Ordered Triple is a Solution:
Determining Whether an Ordered Triple is a Solution:
Determining Whether an Ordered Triple is a Solution:
Solutions of a System of Linear Equations with Three Variables
Number of Solutions of a System of Two Linear Equations
Learn After
A project manager is verifying whether a specific resource allocation triple satisfies a system of three linear constraints. The system is defined as follows:
After substituting the values into the first constraint, , the manager calculates that the left side equals 3. Since is a false statement, what is the definitive conclusion regarding the triple ?
A logistics coordinator is verifying whether the resource allocation triple satisfies the following system of linear constraints:
True or False: If substituting the triple into the first constraint equation () results in a false mathematical statement (such as ), the coordinator can definitively conclude that the triple is not a solution to the entire system without testing the remaining two equations.
A warehouse logistics manager is verifying whether the shipment parameters satisfy the system constraints, starting with the first constraint equation: . Match each component of this specific evaluation process with its corresponding value or conclusion.
A logistics analyst is verifying whether a specific resource allocation triple satisfies a system constraint represented by the equation . Place the following steps of the verification process in the correct chronological order.
An inventory auditor is evaluating whether the stock adjustment triple satisfies the system constraint . Upon substituting , , and into the left side of the equation, the expression simplifies to ____. Since this value does not equal 2, the triple is immediately rejected as a valid solution.