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Christian95's avatar

How do you solve this?

Asked by Christian95 (3253 points ) December 13th, 2009

3xy-y-21=0

Hard problem.Not homework

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20 Answers

jeffgoldblumsprivatefacilities's avatar

I can simplify it to x = 7+y/y, but that’s as far as I can go.

I should add that Math is definitely not my best subject, so don’t trust my judgment.

eeveegurl's avatar

There are two unknowns – I don’t know if you want us to solve for x, solve for y, or what :/

or it could be something easy and my brain’s just rusty on the math

Mr_Quick's avatar

X=7+y/y is the same as x=8

eeveegurl's avatar

I got x=7/y + ⅓

or y = 21 / (3x-1)

Foolaholic's avatar

@jeffgoldblumsprivatefacilities

But how did you get to the dividing by 3 without ending up with a y/3 somewhere along?
The way I see it;
3xy – y – 21 = 0
3xy – y = 21
you either divide by 3 here and get
xy – (y/3) = 7, or take it a step further first:
3xy = 21 + y
xy = 7 + (y/3)

jeffgoldblumsprivatefacilities's avatar

Ah see, I new I would do something wrong.
I did this:
3xy – y – 21 = 0
3xy – y = 21
xy – y = 7
xy = 7 + y
x = 7 + y/y

I was wrong, I didn’t divide the y by 3.

LostInParadise's avatar

3y(x-1)=21. If x and y need to be positive whole numbers then either y=1 and x=8 or y=7 and x=2

CyanoticWasp's avatar

Given 3xy-y-21=0

Dividing by 3:
xy – y/3 – 7 = 0

Solving for x in terms of y (divide by y):
x – 3 – 7/y = 0
x = 3 + (7/y)

But without another equation, you can’t go much further than to swap terms around more.

eeveegurl's avatar

@LostInParadise – I’m pretty sure it’s y (3x-1) = 21

or it’d be 3y (x-⅓) = 21

CyanoticWasp's avatar

Shoot… I miss ‘edit’ capability. Mine is all wrong.

eeveegurl's avatar

@CyanoticWasp – just refresh the page and you should still have 5–10 minutes to edit!

Foolaholic's avatar

@eeveegurl
alright, I agree with y(3x-1) = 21, but I don’t even know where to take that with getting really messy….

LostInParadise's avatar

I messed up in my previous answer. y(3x-1)=21. There is no solution for positive whole numbers. For any x other than ⅓, you can find a y by using y=21/(3x-1)

Jayne's avatar

@jeffgoldblumsprivatefacilities; also, you didn’t divide the 7 by y.

NaturalMineralWater's avatar

1. Print it out.
2. Set it on fire.

bobbinhood's avatar

Since there are two variables, there is actually an infinite number of solutions to this equation. The graph of the equation is a hyperbola. This link shows the graph of the solution set to 7xy – y – 21 = 0.

Christian95's avatar

ok guys here’s what I find from my teacher.
3xy-y=21
y(3x-1)=21 from here it results that y divides 21,so you obtain this possible solution for y={1,-1,3,-3,7,-7,21,-21}
And now you try every possible y on the equation and you will find that the solutions are:
(y,x)={(-3,-2);(-21,0)}

CyanoticWasp's avatar

@bobbinhood That link to Wolfram alone is worth a GA. I love it!

bobbinhood's avatar

@Christian95 2 things:
1) You said this wasn’t homework.
2) If you had actually given us the problem rather than simply an equation, we would have been much more helpful. What you were really looking for was someone to find the integer solutions to 7xy – y – 21 = 0. If you had said that, I assure you we could have explained how to do the problem. Since you simply said “solve this” and presented us with an equality, all we could do was guess at what you were looking for.

@CyanoticWasp That site is amazing. My stats prof introduced it to us this semester and had us use it to calculate sums (It is a senior-level class, and most of us (though not myself) are finished with our bachelors degree in math after this semester, so having us do them by hand would teach us nothing.). This site is also great. It helped me understand unitary matrices and conjugate transpose since my linear algebra text was sorely lacking on those topics.

Christian95's avatar

@bobbinhood It isn’t homework

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