Question

Solve :--

ax +by =p

bx - ay =q​

Answer 1

Answer:

ax+by=p -(1)

multiply the above equation with 'a' on both sides

(a^2)x+aby=ap -(2)

given bx-ay=q -(3)

multiply above equation with 'b' on both sides

(b^2) x-aby=bq -(4)

add equation (2) and (4)

(a^2) x+aby+(b^2) x-aby=ap+bq

x=(ap+bq) /(a^2+b^2)

substitute x in (1) to get y

a(ap+bq) /(a^2+b^2) + by =p

then y= (p(b^2) - abq) /(a^2+b^2)