Summer Math review: Solve for z

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To solve for z in the equation y^2 + 3yz - 8z - 4x = 0, the correct rearrangement yields z = (y^2 - 4x) / (3y - 8). Initially, there was confusion about the sign of the answer, but it was clarified that the negative was incorrect. The term "alienate" was humorously noted as an unusual way to describe isolating z. This discussion highlights the importance of careful algebraic manipulation in solving equations. Clear communication of mathematical processes can lead to better understanding among peers.
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Homework Statement


solve for z:
y^2+3yz-8z-4x=0

Homework Equations


The Attempt at a Solution


I tried to alienate the z
I got the answer:
z=(y^2-4x)/(3y-8)
 
Last edited:
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nevermind, i got the answer
 
Then I presume you realized you had the negative of the correct answer.
 
Heqi said:
I tried to alienate the z

haha first time I've seen anyone describe it that way
 

Thread 'Family of lines that are at a distance of 5 from the origin'

I picked up this problem from the Schaum's series book titled "College Mathematics" by Ayres/Schmidt. It is a solved problem in the book. But what surprised me was that the solution to this problem was given in one line without any explanation. I could, therefore, not understand how the given one-line solution was reached. The one-line solution in the book says: The equation is ##x \cos{\omega} +y \sin{\omega} - 5 = 0##, ##\omega## being the parameter. From my side, the only thing I could...
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