# How do you solve this system of equations?

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.

• If $\beta$ and $\gamma$ are your unknowns, then your system ain't linear. – Ivan Neretin Sep 29 '16 at 20:20
• @IvanNeretin Oh yeah, I inadvertently put "linear" in the title. I fixed it. – Jannik Pitt Sep 29 '16 at 20:22
• Have you tried solving the first equation for $\gamma$ and then substituting into the second? – cdwe Sep 29 '16 at 20:24

From the first equation you have $$\gamma=\frac{1-\beta^2}{v\beta}$$
so the second equation becomes: $$c^2(1-\beta^2)=-v^2\beta^2$$
• For $\nu=0$ we have $\beta^2=1$ and $c\gamma=0$. Of course $\beta$ can't be zero. – Dietrich Burde Sep 29 '16 at 21:03