Question

By elimination method

Answer 1

hope this will help you please mark this answer as brainlist

Answer 2

Your Question:

$ax+by=a^{2}........(i) \\ay+bx=b^{2} ........(ii)$

Answer:

Multiplying (i) by b and (ii) by a,

$=> abx+b^{2}y =a^{2}b.......(iii)\\ =>a^{2}y +abx=ab^{2}......(iv)$

Subtracting (iv) from (iii),

$=>abx+b^{2}y -a^{2} y-abx=a^{2}b-ab^{2} \\ =>b^{2}y-a^{2}y= a^{2}b-ab^{2}\\ =>(b^{2}-a^{2})y=ab(a-b)\\=>(b-a)(b+a)y=ab(a-b)\\=>y=\frac{ab}{(b+a)}$

Substituting value of y in (iii),

$=> abx+b^{2}\frac{ab}{b+a}=a^{2}b\\ =>abx+\frac{ab^{3}}{a+b} =a^{2}b\\=>ab[x+\frac{b^{2}}{a+b}] =ab[a]\\=>x=a-\frac{b^{2}}{a+b}\\=>x=\frac{a^{2}+ab-b^{2}}{a+b}$

Hope this answer helps you ^_^ !