Question

4. What is a linear Diophantine equation of two variables? How many solutions can such an equation have? How can the solution(s) be found?

Answer 1

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A Linear Diophantine equation (LDE) is an equation with 2 or more integer unknowns and the integer unknowns are each to at most degree of 1.

Linear Diophantine equation in two variables takes the form of ??+??=?, where ?,?∈ℤ and a, b, c are integer constants. x and y are unknown variables.

A Homogeneous Linear Diophantine equation (HLDE) is ??+??=0,?,?∈ℤ. Note that ?=0 and ?=0 is a solution, called the trivial solution for this equation.

They have infinitely many solutions

Solution can be found by having x=(-b/a)*y and we can put any integer y which also makes x an integer and that would be the solution

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