Classifying Without Graphing
Determine the number of solutions and classify the system without graphing, by comparing slopes and y-intercepts.
First equation: Solve for :
Second equation: Solve for :
Compare slopes and y-intercepts:
- First line: ,
- Second line: ,
Because the slopes are different (), the two lines must intersect at exactly one point.
The system has 1 solution and is consistent and independent.
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 plans represented by the system of equations: 2x + y = -3 and x - 5y = 5. After determining that the lines have different slopes and will intersect at exactly one point, which term should the coordinator use to classify this system?
A business operations analyst is comparing two cost-efficiency models represented by the system of equations {2x + y = -3, x - 5y = 5}. Match each analytical component to its correct value or classification based on the slope-intercept form of these equations.
A logistics manager is comparing two shipping cost models represented by the equations and . After determining that the slopes are different ( and ), the manager identifies that the lines intersect at exactly one point. This means the system is classified as a(n) ________ system.
A business operations analyst is evaluating two resource allocation models represented by the system of equations {2x + y = -3, x - 5y = 5}. After determining that the two lines have different slopes, the analyst classifies the system as both consistent and independent. Is this statement true or false?
A project coordinator is comparing two workflow efficiency models represented by the equations {2x + y = -3, x - 5y = 5}. To determine the relationship between these models without using a graph, arrange the following analytical steps in the correct logical sequence.
Classifying Marketing Outreach Models
Debt Repayment Strategy Analysis
Classifying Resource Allocation Models
A data analyst is evaluating a resource allocation model represented by the equation . To compare this with another model, the analyst must identify the slope () by rewriting the equation in slope-intercept form (). What is the correct slope for this equation?
A business operations manager is analyzing two financial growth models represented by the system of equations {2x + y = -3, x - 5y = 5}. After converting both equations to slope-intercept form, the manager identifies that the first line has a slope of -2 and the second line has a slope of 1/5. Based on the fact that these slopes are different, how many solutions does this system have?