I was solving a question when in the end the author wrote something like this:

What just happened in the end?

$\displaystyle 5x_1 - 2x_2 + x_3 = 0$

$\displaystyle 2x_1 + 2x_3 = 0$

$\displaystyle -x_1 + 2x_2 + 3x_3 = 0$

Solving the first two, we have

$\displaystyle \frac{x_1}{-4} \ = \ \frac{x_2}{2-10} \ = \ \frac{x_3}{4}$

Please can someone explain me this ??

Thanks a lot !!!!