Question

By cross multiplication find x and y if
ax + by = a² + b² and bx - ay = 0​

Answer 1

$\bold{\underline{\underline{\underbrace{Answer}}}}$

x = a and y = b

Step-by-step explanation:

• To find

The value of x and y

⠀

• Given

ax + by = a² + b² (equation 1)

bx - ay = 0 (equation 2)

⠀

• Solution

{Taking equation 2}

$\sf bx - ay = 0$

{Taking ay on RHS}

$\sf bx = ay$

{Dividing both sides by a}

$\sf \frac{bx}{a} = y(equation \: 3)$

{Now substituting the equation 3 in equation 1}

$\sf ax + b( \frac{bx}{a} ) = {a}^{2} + {b}^{2} \\ \\ \sf ax + \frac{ {b}^{2} x}{a} = {a}^{2} + {b}^{2}$

{Taking LCM on LHS}

$\sf \frac{ {a}^{2}x + {b}^{2} x }{a} = {a}^{2} + {b}^{2} \\ \\ \sf \frac{x( {a}^{2} + {b}^{2}) }{a} = ( {a}^{2} + {b}^{2} )$

{Dividing by (a² + b²) both sides}

$\sf \frac{x}{a} = 1 \\ \\ \green{\boxed {\tt{x = a} } }$

{Now substituting the value of x in equation 3}

$\sf \frac{ba}{a} = y \\ \\ \green {\boxed{ \tt{y = b}} }$