How do you solve this system of equations?

Question

How do you solve this system of equations ($c$ and $v$ are constants):

$\beta\left(\beta+v\gamma\right)=1$

$c^2\gamma(\beta+v\gamma)=-v$

I somehow seem to be stuck and just can't figure out how to solve them in an effective way.

Answer 1

Hint:

From the first equation you have $$ \gamma=\frac{1-\beta^2}{v\beta} $$

so the second equation becomes: $$ c^2(1-\beta^2)=-v^2\beta^2 $$