@mathmale Hello! Please lend a hand?

Question

@mathmale  Hello! Please lend a hand?

nicole143 · Answer

I have to classify the system without graphing as either independent, dependent, or inconsistent. I can't remember how..
-x - 3y = 0
x - y = 4               @mathmale

mathmale · Answer

Howdy, Nicole!  Hope you're doing very well!
It's important to know what those three descriptors mean in the content of simultaneous equations.  For lines in the plane, you can expect that a system of equations is independent if the two lines have different slopes.  Know how to determine that?

If one equation is a multiple of the other, then the system is dependent.

If the lines described by the two equations are parallel, but not touching, the system is inconsistent.  

Hope you'll write this stuff down for reference.  All the best to you.  MM

nicole143 · Answer

Thank you! I hope you are doing good as well(:

mathmale · Answer

Just fine, nicole, and thank you very much.  Went to visit my 97-year-old mother today.

nicole143 · Answer

Goodness, I hope she is very well! 
How do you know without graphing if they will touch or not? @mathmale