How to Solve for x or y in a Horizontal Tangent Problem?

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Homework Help Overview

The discussion revolves around solving the equation 4x - 2xy = 0 for either variable x or y. Participants are exploring the implications of the equation and the conditions under which solutions can be derived.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss their attempts to isolate y and the challenges faced when substituting values back into the original equation. There is a focus on whether x can be canceled out and the implications of that on finding solutions.

Discussion Status

Some participants have provided alternative interpretations of the equation and suggested potential values for x and y. There is an ongoing examination of the correctness of these values, but no consensus has been reached on a definitive solution.

Contextual Notes

Participants are working within the constraints of the original equation and are questioning the validity of their assumptions regarding variable cancellation and the resulting values.

brambleberry
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Homework Statement



4x - 2xy = 0
how do i solve for EITHER x or y?

Homework Equations





The Attempt at a Solution



i got y = 2 at first but when i plugged it into the original equation to find x it was impossible to get an answer (the x's canceled out)
 
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brambleberry said:
i got y = 2 at first but when i plugged it into the original equation to find x it was impossible to get an answer (the x's canceled out)

the x doesn't cancel out.

4x-2xy=0
2x(2-y)=0

so 2x=0 or 2-y=0.

Meaning x=0,y=2
 
rock.freak667 said:
the x doesn't cancel out.

4x-2xy=0
2x(2-y)=0

so 2x=0 or 2-y=0.

Meaning x=0,y=2

the original equation is 2y^3 + 6(x^2)y - 12x^2 + 6y = 1
 
4x-2xy=0
4x=2xy
4=2y
2=y
4x-2x(2)=0
4x=2x(2)
4x=4x
x=1
4(1)-2(1)(2)
4-4=0
yeah i think that's right but not 100% sure
 

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