Question 507175
<pre>
What you did was mathematically correct but it doesn't help
isolate y.

    x² + xy + y² = 9

First get 0 on the right

x² + xy + y² - 9 = 0

Rearrange in descending powers of y:

y² + xy + x² - 9 = 0 

Think of it as a quadratic equation in y this way:

1y^2 + xy + (x²-9) = 0

Then use the quadratic formula 

{{{y = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}

where a = 1, b = x, c = (x²-9)

{{{y = (-(x) +- sqrt((x)^2-4*(1)*(x^2-9) ))/(2*(1)) }}}

{{{y = (-x +- sqrt(x^2-4(x^2-9)))/2 }}}

{{{y = (-x +- sqrt(x^2-4x^2+36))/2 }}}

{{{y = (-x +- sqrt(-3x^2+36))/2 }}}

{{{y = (-x +- sqrt(36-3x^2))/2 }}}

Edwin</pre>