functions: determining if y is an implicit function of x

[berni2723]

my professor gave an example for fun and its killing me that i cant solve it....
the equation y^2+5xy-3x+2=0, to determine whether y is implicitly a function of x, i tried to get y by
itself, i'm having a hard time with that and want to just check with those who know better to make sure i'm not just beating a dead horse here...thank you whoever takes the time to respond!!!

 

[lookagain]

the equation y^2+5xy-3x+2=0, ..., i tried to get y by itself, ...

\(\displaystyle Rewrite \ \ y^2 + 5xy - 3x + 2 = 0 \ \ as\)


\(\displaystyle y^2 + (5x)y - (3x - 2) = 0.\)



\(\displaystyle \text{For the Quadratic formula, substitute for these:}\)


\(\displaystyle a = 1\)

\(\displaystyle b = 5x \)

\(\displaystyle c = -(3x - 2)\)