Question

a/x -b/y=0
ab2/x+a2b/y=a2+b2

Answer 1

$Given\ \frac{a}{x}=\frac{b}{y}\\\\Given\ \frac{ab^2}{x}+\frac{a^2b}{y}=a^2+b^2\\\\ \implies\frac{ab^2}{x}+a^2 \frac{a}{x}=a^2+b^2\\\\ \implies \frac{a}{x}(a^2+b^2)=a^2+b^2\\\\x=a\\\\ \implies y=b$

Answer 2

Answer:

value of x = a and y = b

Step-by-step explanation:

Given System of equations:

$\frac{a}{x}-\frac{b}{y}=0$ ....................(1)

$\frac{ab^2}{x}+\frac{a^2b}{y}=a^2+b^2$ ..................(2)

Given equations are not linear.

let, 1/x = u and 1/y = v

we get

au - bv = 0 .....................(3)

ab²u + a²bv = a²+b² ................(4)

from equation 3,

u = bv/a

put this in eqn (4)

$ab^2\times\frac{bv}{a}+a^2bv=a^2+b^2$

$b^3v+a^2bv=a^2+b^2$

$(b^2+a^2)bv=a^2+b^2$

$v=\frac{1}{b}$

$u=\frac{b\times\frac{1}{b}}{a}=\frac{1}{a}$

So, 1/x = 1/a  ⇒ x = a

and 1/y = 1/b ⇒ y = b

Therefore, value of x = a and y = b