If (x0,y0)=(1,1)(x_0, y_0) = (1, 1)(x0,y0)=(1,1) is a particular solution to 2x+5y=72x + 5y = 72x+5y=7, what is the general solution?
(x,y)=(1+5t,1−2t)(x, y) = (1 + 5t, 1 - 2t)(x,y)=(1+5t,1−2t) for all integers ttt
(x,y)=(1+2t,1+5t)(x, y) = (1 + 2t, 1 + 5t)(x,y)=(1+2t,1+5t) for all integers ttt
(x,y)=(1−5t,1+2t)(x, y) = (1 - 5t, 1 + 2t)(x,y)=(1−5t,1+2t) for all integers ttt
Only (1,1)(1, 1)(1,1) works