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Checking an Ordered Pair as a Solution to a Linear Equation in Two Variables
To determine if an ordered pair is a solution to a linear equation in two variables, substitute the - and -values from the ordered pair into the equation. If the substitution results in a mathematically true statement, the ordered pair is a solution. If it results in a false statement, the ordered pair is not a solution.
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Intermediate Algebra @ OpenStax
Ch.3 Graphs and Functions - Intermediate Algebra @ OpenStax
Algebra
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System of Linear Equations
Verifying Whether and are Solutions of
Determining Whether Ordered Pairs are Solutions of
A warehouse supervisor uses the linear equation 40x + 60y = 2400 to manage the weight of two types of cargo on a pallet. Based on the mathematical definition, which of the following describes when an ordered pair (x, y) is a solution to this equation?
A retail manager uses the linear equation 20x + 50y = 1000 to manage inventory costs. An ordered pair (x, y) is a ____ of this equation if substituting the values for x and y results in a true numerical statement.
A small business owner uses the linear equation 15x + 25y = 300 to manage the monthly budget for office supplies (x) and cleaning services (y). True or False: An ordered pair (x, y) is defined as a solution to this equation if substituting the specific values for x and y into the equation results in a true numerical statement.
A production manager uses a linear equation to ensure that the combination of two different resources (x and y) meets a specific output target. To verify if a proposed resource allocation plan, represented as an ordered pair (x, y), is a valid solution to the production equation, arrange the following verification steps in the correct order.
Defining Solutions in Logistics Management
In a project management scenario, a lead planner uses linear equations to balance the allocation of two different types of staff (Type X and Type Y). Match each algebraic term below with the definition that correctly describes its role in verifying resource allocation plans.
Defining Solution Verification in Professional Modeling
Verifying Staffing Solutions in Retail Management
A hospital administrator uses the linear equation $500x + 300y = 15000xy(x, y)$, to be considered a solution to this equation?
Defining Solution Verification in Logistics
Graph of a Linear Equation in Two Variables
Determining Whether Ordered Pairs are Solutions of
Solution to a Linear Inequality in Two Variables
Checking an Ordered Pair as a Solution to a Linear Equation in Two Variables
Example: Evaluating Ordered Pairs for a Linear Equation
Learn After
A business analyst needs to verify if a specific data point, represented as an ordered pair , is a valid solution to a company's revenue equation. Arrange the following steps in the correct order to perform this check.
A quality control technician uses a linear equation to model the relationship between the weight () and volume () of a liquid chemical batch. To verify if a specific recorded data point is a valid 'solution' to this equation, what is the fundamental requirement that must be met after the technician substitutes the coordinates into the equation?
An accounting specialist is checking if a specific expense report data point (, ) satisfies a linear budget model. If substituting the coordinates of the ordered pair into the model results in a mathematically false statement, the ordered pair is NOT a solution to the equation.
A data analyst is verifying if a specific coordinate pair satisfies a linear trend equation used for sales forecasting. Match the following terms used in the verification process with their correct descriptions.
A logistics coordinator is testing a data point, formatted as an ordered pair, against the supplier's linear freight equation. To confirm that the ordered pair is a solution, the coordinator substitutes the values into the equation and verifies that it produces a mathematically ____ statement.