Question

1. Solve the following system of equations for x:

(b2/a)x –(a2/b)y = ab(a+b)
b2x – a2y = 2a2b2

Answer 1

Ans :

$x = {a}^{2}$

Answer 2

The solution for x is x = a².

Step-by-step explanation:

The system of linear equations with variables x and y are given to be

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

⇒ b³x - a³y = a²b²(a + b) .......... (1)

⇒ b³x - a³y = a³b² + a²b³ ........... (2)

And, the other equation is

b²x - a²y = 2a²b² ............ (3)

⇒ b³x - a²by = 2a²b³ ............ (4)

Now, solving equations (2) and (4) we get,

a²by - a³y = a³b² + a²b³ - 2a²b³ = a³b² - a²b³

⇒ a²(b - a)y = a²b²(a - b)

⇒ y = - b²

Now, from equation (3) we get

b²x - (-b²)a² = 2a²b²

⇒ b²x = a²b²

⇒ x = a²

Therefore, the solution for x is x = a². (Answer)