Solving congruences and diophantine equations in number theory

[trees and plants]

Hello. I do not understand how to solve systems of three or two congruences of one unknown of first order, a congruence of one unknown of second order and a system of diophantine equations of two or three unknowns. Could someone help me by providing examples in these cases? Thank you.

 

[Office_Shredder]

Why don't you post an example of an equation and what you don't understand about how to solve it

 

[trees and plants]

Solve the system 8x ≡ 4(mod20), 15x ≡ 10(mod35), 9x ≡ 12(mod39). As well, if you can tell me how to apply it to other similar situations. Find also the solutions of the system x ≡ 1(mod15), x ≡ 7(mod18). Thank you.

 

[hutchphd]

I enjoy systems of equations such as these. They remind me of a multifaceted gem.