Question

Prove that ax+by=a+c is solvable if and only if ax+by =c is solvable

Answer 1

Given:

ax+by=a+c is solvable

To find:

if and only if ax+by =c is solvable

Solution:

Let,

ax + by = b + c

Then the above equation has a solution: (x, y).

(x, y-1) is a solution of: ax + by = c.

 If ax + by = c has a solution of: (x, y).

Then, (x, y+1) is a solution of: ax + by = b + c.

That's why the given value is its solution.