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.