Question

cross multiplication method ax +by=c and bx+ay= 1+c

Answer 1

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 )}