Question

(ax/b)-(by/a)=a+b and. ax-by=2ab find the value of a and b

Answer 1

Answer:

Given system of equations:

{ax}/{b}-{by}/{a}=a+b ...................... (1)

ax-by=2ab ....................(2)

from equation (2), we get

ax=2ab+by

x={2ab+by}/{a} ......... (3)

Put, this value of eqn (3) in eqn(1)

(a* {2ab+by}/{a})/{b}-{by}/{a}=a+b

{2ab+by}/{b}-{by}/{a}=a+b

{a(2ab+by)-b^2y}/{ab}=a+b

2a^2b-aby+b^2y=ab(a+b)

2a^2b+(ab-b^2)y=a^2b+ab^2

(ab-b^2)y=a^2b+ab^2-2a^2b

b(a-b)y=ab^2-a^2b

b(a-b)y=-ab(a-b)

y={-ab(a-b)}/{b(a-b)}

y=-a

Now, Put value of y in eqn (3)

x={2ab-ba}/{a}

x={ab}/{a}

x=b

Therefore, x = b & y = -a