Question

solve for x and y
$\frac{x}{a} - \frac{y}{b} = 0 \: \: ax + by = {a}^{2} + {b}^{2}$
​

Answer 1

SOLUTION:-

We have,

$\frac{x}{a} - \frac{y}{b} = 0 \\ \\ = > bx - ay = 0......(1) \: \: \: \: \: \: [cross \: multiplication]$

ax + by= a² + b²............(2)

Therefore,

Lets multiply equation (1) by b & (2) by a so that variable y in both the equation have same coefficient.

=)b²x -aby =0

=)a²x+ aby =a³ + ab²

_____________________

=) b²x +a²x + 0= a³ +ab²

So,

=) b²x + a²x= a³ + ab²

=) x(b² + a²) =a(b²+a²)

=) x= a

Substitute x = a in equation (1), we get;

=) ab - ay=0

=) ay= ab

=) y= b

Hence,

x = a & y= b.

Hope it helps ☺️