x/a-y/b=0 and ax+by=a^2+b^2.Solve by Elimination Method.

x/a-y/b=0 and ax+by=a^2+b^2.Solve by Elimination Method. [ICSE Class 9 ML Aggarwal Solution Chapter-5 Exercise 5.2 Question number 9(ii) Simultaneous Linear Equations ]

$\frac{x}{a} – \frac{y}{b}$ = 0 —-(i)

ax+by=a²+b² —(ii)

From equation (i) we get,

bx-ay=0 —-(iii)

Now multiplying equation (iii) with b and equation (ii) with a we get,

a²x+aby=a³+ab² —-(iv)

b²x-aby=0 —(v)

adding (iv) and (v) we get,

a²x+b²x= a3+ab²

⟹ x(a²+b²) = a(a²+b²)

⟹ x = $\frac{a\left(a^2 + b^2\right)}{\left(a^2 + b^2\right)}$

⟹ x =a

Substituting value of x in equation (iii) we get,

b(a)-ay=0

⟹ ab=ay

⟹ y = b

Therefore Required Solutions are x = a and y=b.