two equations =0, finding x and y

Question

anna_1313 · Answer

attachment

anna_1313 · Answer

this gives x=6 and y=2, i dont know how to get that

.alex · Answer

did you try substitution

anna_1313 · Answer

its gives a complicated equation

mathmale · Answer

True.  So what are y ou going to do?

Why not mult. all 3 terms of the 2nd equatio by y^2.

Doing so should give you $$4xy^2-96=0,$$

mathmale · Answer

Divide both sides by 4 and reduce everything as far as possible.

mathmale · Answer

Solve the resulting equation for x.
Square both sides of this x.

This will give you x^2.

Substitute your result into the first equation.  This will enable you to eliminate x^2.

Solve the resulting equation for y^2, and then for y.

agent0smith · Answer

Substitution doesn't look that hard 
$\Large 4y - \frac{ 288 }{x^2  } =0$              $\Large 4x - \frac{ 96 }{y^2  } =0$
Solve the 2nd for x and plug into the first 
$\Large x = \frac{ 24 }{y^2  } $

$$\large 4y - \frac{ 288 }{\frac{ 24^2 }{ y^4 }  } =0$$ $$\large 4y - \frac{ y^4 }{2}  =0$$ $$\large y(4- \frac{ y^3}{2} ) =0$$Easy to solve from there.