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January 31, 2015

January 31, 2015

Posted by **Gina** on Saturday, September 13, 2008 at 6:13pm.

x^2y-x^2+4y=0

Please help. Thanks.

- pre-calculus -
**David Q**, Saturday, September 13, 2008 at 6:23pmDo you mean "Can y be expressed as a function of x?". If so then the answer is yes it can, if by "x^2y" you mean "x²y" and not "x raised to the power of 2y". The equation x²y - x² + 4y = 0

can be written as (x²+4)y = x², from which you can easily express either x in terms of y, or y in terms of x.

- pre-calculus -
**Damon**, Saturday, September 13, 2008 at 6:28pmwell, you can write y as a function of x, and get one and only one value of y for every x

however x is not a function of y because there are two values of x for every y.

- pre-calculus -
**David Q**, Saturday, September 13, 2008 at 6:42pmFair enough, though you could presumably define a function by restricting the range to just zero plus either the positive or negative real numbers.

- pre-calculus -
**Gina**, Saturday, September 13, 2008 at 7:17pmSo the answer is yes?

- pre-calculus -
**David Q**, Sunday, September 14, 2008 at 6:00amThe answer is yes: you can write y as a function of x. Damon and I were debating whether you can write x as a function of y, which wasn't what you were asked.

- pre-calculus -
**Gina**, Sunday, September 14, 2008 at 11:28amHow exactly do you know that you can get one and only one value of y for every x?

- pre-calculus -
**Anonymous**, Sunday, September 14, 2008 at 12:27pmThere's only one value for y because your original equation (x^2y-x^2+4y=0) can be rewritten as (x²+4)y = x². Or, by dividing both sides by (x²+4),

y = x²/(x²+4)

Feed any value of x into the right-hand side, and you'll get exactly one value for y.

- pre-calculus -
**Gina**, Sunday, September 14, 2008 at 2:19pmOH thanks, gotcha!

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