Question

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

Answer 1

Answer:

$\frac{x}{a} + \frac{y}{b} = 2$

Multiply by ab on both sides , we get

$bx + ay = 2ab$

We have

$bx + ay = 2ab \: and \: ax - by = {a}^{2} - {b}^{2}$

as a pair of linear equations. Multiply first equation by a and second equation by b so then after performing this we get

$abx + {a}^{2} y = 2 {a}^{2} b$

and

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

Subtract second equation from first equation, we get

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

$= > y = b$

Substitute y => b in first equation,we get

$bx + a \times b = 2ab = > bx = 2ab - ab$

$= > bx = ab = > x = a$

So the solution for this pair of equations =>

x = a and y = b. Hope it helps you.