Question

b2x/a+a2y/b=ab(a+b) and b2x+a2y=2a2b2 solve for x and y​

Answer 1

See the pictures

Solved by cross multiplication method

Answer is x= a² and y= -b²

Answer 2

The value of x and y are $a^{2} \ and \ b^{2}$ respectively.

Step-by-step explanation:

Given:

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

Equation $b^{2} x+a^{2} y=2a^{2} b^{2}$.

To Find:

The value of x and y.

Solution:

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

$\frac{b^{2} }{a} x+\frac{a^{2} }{b} y=ab(a+b)$ ------------- equation no.01.

$b^{3}x+a^{3} y=a^{2}b^{2} (a+b)$

$b^{3}x+a^{3} y=a^{3}b^{2} + a^{2} b^{3}$   ------------------- equation no.02.

As given-equation $b^{2} x+a^{2} y=2a^{2} b^{2}$.

$b^{2} x+a^{2} y=2a^{2} b^{2}$  -------------- equation no.03.

$b^{2} x=2a^{2} b^{2} -a^{2} y$

$x=\frac{2a^{2} b^{2} -a^{2} y}{b^{2} }$

Putting the value of x in equation no.03, we get.

$b^{3} (\frac{2a^{2} b^{2} -a^{2} y}{b^{2} } )+a^{3} y=a^{3}b^{2} + a^{2} b^{3}$

$b( {2a^{2} b^{2} -a^{2} y)+a^{3} y=a^{3}b^{2} + a^{2} b^{3}$

$( {2a^{2} b^{3} -a^{2}b y)+a^{3} y=a^{3}b^{2} + a^{2} b^{3}$

$-a^{2}b y+a^{3} y=a^{3}b^{2} + a^{2} b^{3}- {2a^{2} b^{3}$

$a^{2} (a-b)y= a^{3}b^{2} - a^{2} b^{3}$

$a^{2} (a-b)y=a^{2}b ^{2} (a-b)$

$y=b^{2}$

Putting the value of y in equation no.03 , we get.

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

$b^{2} x=2a^{2} b^{2}-a^{2} b^{2}$

$b^{2} x=a^{2} b^{2}$

$x=a^{2}$

Thus,the value of x and y are $a^{2} \ and \ b^{2}$ respectively.

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