Help needed regarding homogenous equations in algebra.

I have just started with algebra and I see here something about homogenous equations but I am just not able to figure it out. I read this answer here,

Homogenous equation in linear algebra?

But still, I couldn't figure it out, what it really means. Here is a photograph of what my book says. If possible please explain it to me! Also i read on google, there is something like non- homogenous equation too. Please explain to me that also.

Thanks a lot!

• How old is this book ? 1887 ? Can you please tell me the title and author? Sep 19, 2016 at 22:27
• @ReneSchipperus Hi! The book's name is "Higher Algebra" by Hall and Knight. And yeah, year was 1887. Sep 19, 2016 at 22:36
• And you got it from internet archive ? (a great site !) Sep 19, 2016 at 22:38
• Haha, no i actually have a copy of that. I downloaded it so that i can ask questions here on MSE ( by taking screenshots of the pages ) as i have no teacher to explain to me all the stuff that i read. Here's the link to the pdf forgottenbooks.com/en/download/HigherAlgebra_10021865.pdf Sep 19, 2016 at 22:48
• Reading such an old book might be a bit hard for a beginner. Personally I like those books, but I first learnt from more modern sources. What is your ultimate goal ? Sep 19, 2016 at 22:59

A monomial in several variables has a degree, the sum of all the individual degrees. For example all of the following are degree $3$. $$x^3,y^3,x^2y,xyz.$$
The book is saying that if $P(x,y,z)$ is homogenous then say if degree $k$, then $$P(ax,ay,az)=a^kP(x,y,z)$$ So multiplying the variables by a constant $a$ does not change an equation $P(x,y,z)=0$.