Solve the given simultaneous equations in x^2, x and y

[chwala]

Homework Statement

See attached

Relevant Equations

Simultaneous equations

In my approach i have,

$\dfrac{x^2}{4} -1 = \dfrac{1}{y+1}$

$9-\dfrac{3}{2}=\dfrac{1}{y+1}$

then,

$\dfrac{x^2}{4} -1= 9-\dfrac{3}{2}$

$x^2-4=36-6x$

$x^2+6x-40=0$

$x_1=4, x_2=-10$

it follows that when $x=4$ then $y+1=\dfrac{1}{3}$ ⇒$y=-\dfrac{2}{3}$

and when $x=-10$ then $y+1=\dfrac{1}{24}$ ⇒$y=-\dfrac{23}{24}$

Seeking alternative ways...

 

[haruspex]

I see no reason to hope there is a quicker way. Btw, you seem to have dropped 'x' in a couple of places when typing your post.