Given, ax + by = c    ..............1

and bx + ay = 1 + c  ..............2

Multiplied by b in equation 1 and a in equation 2, we get

abx + b² y = bc    ..................3

abx + a² y = a + ac  ..............4

Subtract equation 3 and 4, we get

      b² y - a² y = bc - a - ac

=> (b² - a² )y = (bc - a - ac)

=> y = (bc - a - ac)/(b² - a² )

From equation 1, we get

     ax + b * (bc - a - ac)/(b² - a² ) = c

=> ax = c - b * (bc - a - ac)/(b² - a² )

=> ax = c - (b² c - ab - abc)/(b² - a² )

=> ax = {c(b² - a² ) - (b² c - ab - abc)}/(b² - a² )

=> ax = {cb² - ca²  - b² c + ab - abc)}/(b² - a² )

=> x = {cb² - ca²  - b² c + ab - abc)}/{a(b² - a² )}