The general solution to the linear Diophantine equation 3x+5y=23x + 5y = 23x+5y=2 in integers is:
x=4+5t,y=−2−3tx = 4 + 5t, y = -2 - 3tx=4+5t,y=−2−3t (any integer ttt)
x=−1+5t,y=1−3tx = -1 + 5t, y = 1 - 3tx=−1+5t,y=1−3t (any integer ttt)
x=2+5t,y=−1−3tx = 2 + 5t, y = -1 - 3tx=2+5t,y=−1−3t (any integer ttt)
No integer solutions exist