Linear Diophantine Equation: Solve using Division ALG and Basic Properties of Numbers

We used the idea of the division ALG and the basic properties of numbers such as additivity and multiplication to solve equation.

UPDATE: To clarify, (If m divides the expression) if m | a - b, then, km = a - b, which gives km + b = a (division ALG). Then consider, k = 1 and b = 0, for, km = a = 2a - a = m.

At the start, the left side equation can be solved because x and y are terms of each other by x = y = -k.

Source: Vladimir Sharich from the YT channel with the same name.