Intercept question (manipulating equations)

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SUMMARY

The discussion centers on finding the x and y intercepts of the equation 1/x = 1/y. It concludes that the intercepts are undefined because the equation is not well-defined at x = 0 and y = 0. The correct interpretation is that while one might consider cross-multiplying to derive x = y, this manipulation does not apply since it leads to an undefined state at the origin. Therefore, the curve represented by the equation behaves like the line y = x, excluding the origin where intercepts do not exist.

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mattmns
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I saw this question yesterday.

Find the x and y intercepts of:

1/x = 1/y
--------

In this case are the intercepts undefined? Or can I cross multiply and get x = y, and then the intercepts are 0 and 0? Also, if I cannot cross multiply, or maniuplate the equation, does that mean that anytime you are not allowed to have x = 0, or y = 0 as values in the original equation, then the respective intercept is undefined?

Thanks!
 
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The curve defined by that equation is the line y=x minus the point at the origin, so it has no intercepts. The equality simply doesn't hold (since the equation isn't well defined) at x=y=0.
 

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