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Explain why it makes sense that a system of two lines with equal slopes but different y-intercepts has no solutions.

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Answer:

Please check explanations

Explanation:

Here, we want to seek why the system has no solutions

An example is necessary

Let us have two lines with equal slopes and different y-intercepts

y = 2x + 5

y = 2x - 3

To solve this system, we equate the y-values

2x + 5 = 2x - 3

The reason why this has no solution is that there is no x value that would validate the equality

It is impossible to find an x value which when inserted would make both equations equal

In the absence of this, we can make that conclusion that the system of equations has no solution

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