Question

Q2. Prove that ax + by = a + c is solvable if and only if
Progress
Q1. Show that all solutions of 3x + 5y = 1 can be written in
the form x = 2 + 5t, y = -1 -3t;
ax + by = c is solvable.
Q3. Find all solutions in positive integers of 5x + 3y = 52.
Q4. Prove that the Diophantine equation ax + by = c has a
solution if and only if gcd(a, b) c. (5marks) ​

Answer 1

Answer:

The condition that the equation

ax? +2hxy + by? +2gx +2fy+c=0, can take

the form ax? +2hXY+bY? = by translating

the origin to a suitable point is