Characteristic equations from Arrigo "An Introduction to Partial Differential Equations" Chapter 2 Exercise

Question

I'm recently reading the Arrigo "An Introduction to Partial Different Equations" and I saw this problem in the book. Exercise 2.6 of Chapter 2.
$$\frac{dx}{a(x,y,u)}=\frac{dy}{b(x,y,u)}=\frac{du}{c(x,y,u)}=\frac{d(\alpha a+\beta b+\gamma c)}{\alpha a+\beta b+\gamma c}$$ The last term of the equation is not explained clearly in the book, and the author applied it in one of the examples in the chapter.
Can someone teach me how to prove this equation? Thank you very much.