ax + by= c  …………………(i)

bx + ay = 1+ c  ………… ..(ii)

Multiplying a to equation (i) and  b to equation (ii), we obtain

a²x + aby = ac ………………… (iii)

b²x + aby = b + bc  …………… (iv)

Subtracting equation (iv) from equation (iii),

(a² – b²) x = ac − bc– b

x = (ac − bc– b)/ (a² – b²)

x = c(a-b) –b / (a²+b²)

From equation (i), we obtain

ax +by = c

a{c(a−b)−b)/ (a² – b²)} +by=c

ac(a−b)−ab/ (a² – b²)+by=c

by = c–ac(a−b)−ab/(a² – b²)

by = abc – b² c+ab/a²-b² 

y = c(a + b) + a/a²-b²