Consistent System of Equations
A consistent system of equations is a system of equations that has at least one solution. When the equations in the system are graphed, the lines either intersect at a single point — giving exactly one solution — or lie directly on top of each other as coincident lines — giving infinitely many solutions. In both cases, there is at least one ordered pair that satisfies every equation in the system simultaneously.
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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.
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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
In a professional budget analysis, if a system of linear equations is described as 'consistent', which of the following must be true about its solutions?
In a professional resource allocation model, a system of linear equations that has at least one solution is classified as a(n) ____ system.
In a corporate resource allocation graph, if two lines representing a system of equations lie directly on top of each other, the system is classified as 'consistent'.
As a business analyst, you are modeling resource constraints using systems of linear equations. Match each system classification or graphical outcome with the description that best defines its results regarding the number of solutions.
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In a corporate resource allocation model, an analyst must verify if a system of linear equations is 'consistent' to confirm that at least one feasible solution exists. Arrange the steps of the classification process in the correct logical order, starting with the initial observation.
A business analyst is reviewing a graph of two linear equations that model different departmental budgets. If the analyst labels the system as 'consistent' in the summary report, which graphical observation would justify this term?
In a corporate resource allocation model, a system of linear equations is described as consistent. Which of the following graphical outcomes is impossible for this type of system?
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