Independent Equations in a Linear System
Two equations in a system of linear equations are independent if they each have their own distinct set of solutions — that is, neither equation is a multiple or rearrangement of the other. When graphed, independent equations produce either two intersecting lines (sharing exactly one common solution) or two parallel lines (sharing no common solutions). In both cases, the lines are geometrically separate objects rather than the same line drawn twice.
0
1
Tags
OpenStax
Elementary Algebra @ OpenStax
Ch.5 Systems of Linear Equations - Elementary Algebra @ OpenStax
Algebra
Math
Prealgebra
Intermediate Algebra @ OpenStax
Ch.4 Systems of Linear Equations - Intermediate Algebra @ OpenStax
Related
Consistent System of Equations
Inconsistent System of Equations
Independent Equations in a Linear System
Dependent Equations in a Linear System
Classifying Without Graphing
Classifying Without Graphing
Classifying Without Graphing
A business analyst is comparing the projected revenue of two different product lines by graphing their growth equations on a coordinate plane. Match the visual behavior of the lines on the graph to the number of solutions for the system.
A business analyst is comparing the projected revenue of two different product lines by graphing their growth equations on a coordinate plane. Match the visual behavior of the lines on the graph to the number of solutions for the system.
A quality control analyst is comparing the performance of two production lines using linear equations. If the analyst determines that the equations representing the production rates have the same slope but different y-intercepts, how many points of equality (solutions) does this system have?
A business analyst is evaluating two different revenue models. If both models are represented by the exact same line on a coordinate plane (coincident lines), the system of equations is said to have ____ solutions.
A financial analyst is comparing two cost-projection models represented by linear equations. If the analyst finds that both equations have the same slope but different y-intercepts, the system of equations has no solution.
A business analyst is categorizing pairs of linear models by the number of points where they are equal (solutions). Arrange these scenarios in order from the case with the FEWEST solutions to the case with the MOST solutions.
Conditions for Parallel Resource Models
Classifying Linear Models in Business Analysis
Cloud Storage Pricing Comparison
A financial analyst is comparing several pairs of cost-projection models represented by linear equations. Match each algebraic relationship between the models' slopes and y-intercepts to the resulting number of points where the two models will have equal costs (the number of solutions).
Learn After
A logistics coordinator is comparing two different delivery route cost models using a system of linear equations. If the coordinator determines that the equations are 'independent', which of the following describes the graphical relationship between the two lines?
A financial analyst is comparing two revenue streams using a system of linear equations. If the equations are independent, then neither equation is a multiple or rearrangement of the other.
In a professional resource planning scenario, two linear equations are described as ____ if neither equation is a mathematical multiple or a rearrangement of the other.
A technical analyst is classifying linear systems used in a resource allocation project. To ensure the models are correctly identified, match each characteristic of 'independent equations' with its corresponding mathematical or graphical description.
Characteristics of Independent Equations in Systems
Categorizing Operational Models in Business Analytics
Explaining Independent Equations in Operational Modeling
An operations manager is training a new analyst to distinguish between different types of mathematical models. Arrange the steps the analyst should take to confirm that two equations in a linear system are 'independent' based on the standard definition.
A business analyst is comparing two different market growth projections using a system of linear equations. If the analyst classifies these equations as independent, which of the following describes the possible number of common solutions the two models can share?
A technician is evaluating two different resource allocation models represented by a system of linear equations. If the technician confirms that these equations are independent, which of the following is a defining graphical characteristic of the system?