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7.8 Identify Structure In a system of two equations, the graph of one line has a ositive slope and the graph of the other line has a negative slope. What can you onclude about the system?

Ask by Erickson Goodwin. in the United States
Feb 28,2025

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Answer

The system has one unique solution because the lines intersect at exactly one point.

Solution

Since one line has a positive slope and the other has a negative slope, the lines are not parallel. This means they will intersect (and do so at exactly one point). In other words, the system is consistent and independent—it has a unique solution.

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Bonus Knowledge

When you have two lines with one having a positive slope and the other a negative slope, you can expect that these lines will intersect at some point. This means that the system of equations you are dealing with is consistent and independent, which indicates there is a unique solution. So, get ready to find that intersection point—it’s where both equations meet and balance out! This type of scenario is super common in real life! Think about mixing two products or services that benefit from each other; maybe one product attracts a customer base while the other provides a unique offering. Their balance point (or intersection) can help businesses determine optimal pricing strategies or resource allocations. So, whether it’s math or business, those intersections could lead to exciting solutions!

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