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11. BUSINESS The number of items sold at Store 1 can be represented by \( y=200 x+300 \), where \( x \) represents the number of days and \( y \) represents the number of items sold. The number of items sold at Store 2 can be represented by \( y=200 x+100 \), where \( x \) represents the number of days and \( y \) represents the number of items sold. Look at the graph of the system of equations and determine whether it has no solution, one solution, or infinitely many solutions.

Ask by Bright Weston. in the United States
Mar 09,2025

Upstudy AI Solution

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Answer

The system of equations has no solution because the lines representing the number of items sold at Store 1 and Store 2 are parallel and distinct.

Solution

1. Identify the equations: - For Store 1: \( y = 200x + 300 \) - For Store 2: \( y = 200x + 100 \) 2. Compare the slopes: Both equations have the same slope of \(200\). This indicates that the lines are parallel. 3. Compare the y-intercepts: - Store 1 has a y-intercept of \(300\). - Store 2 has a y-intercept of \(100\). Since the y-intercepts are different, the lines are distinct. 4. Conclusion: Since the lines are parallel and distinct, they do not intersect. Therefore, the system of equations has no solution.

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Bonus Knowledge

In this scenario, both equations represent straight lines, and when graphed, they will provide insight into the relationship between the two stores. Since both lines have the same slope of 200, they are parallel to one another. However, their y-intercepts differ (300 for Store 1 and 100 for Store 2), which means they will never intersect. Therefore, the system of equations has no solution, as the lines do not meet at any point. To understand this concept further, remember that when two lines are parallel, they indicate that two different situations are progressing at the same rate but starting from different points. This can commonly be applied in business scenarios, where competing stores are frequently increasing sales at the same pace but may have different strategies or starting statistics that affect overall performance. Understanding this can help businesses strategize effectively, recognizing where adjustments might be needed to gain a competitive advantage.

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