Question

solve for x and y x/a+y/b=2 ax-by=a²-b²

Answer 1

HELLO DEAR,

x/a + y/b = 2
${\Rightarrow }$ay + xb = 2ab----------( 1 )

ax - by = a² - b²---------( 2 )

from-----( 1 ) &-------( 2 )
multiply ( 1 ) by "a" ( 2 ) by "b"

abx + a²y = 2a²b
abx - b²y = ba² - b³
-------------------------------------------------
y(a² + b²) = 2a²b - ba² + b³

${\Rightarrow }$y(a² + b²) = a²b + b³

${\Rightarrow }$y(a² + b²) = b(a² + b²)

${\Rightarrow }$y = b [ put in -----( 1 )]

we get,

${\Rightarrow }$ay + xb = 2ab

${\Rightarrow }$a(b) + xb = 2ab

${\Rightarrow }$xb = 2ab - ab

${\Rightarrow }$x = ab/b

${\Rightarrow }$x = a


I HOPE ITS HELP YOU DEAR,
THANKS

Answer 2

Answer:

X/a+y/b=2

Bx+ay/ab=2 (Lcm)

Bx+ay=2ab (*a) ...(I)

Ax-by=a^2-b^2 (*b)... (II)

Eliminating eq(ii) from eq(i)

Abx+a^2y=2a^2b

Abx-b^2y=a^2b-b^3

- + -

------------------------------------

A^2y+b^2y=2a^2b-(a^2b-b^3)

y(a^2+b^2)= 2a^b-a^2b+b^3

y(a^2+b^2)= a^2b+b^3

y(a^2+b^2)= b(a^2+b^2)

y = b... (III)

Putting eq(iii) in eq(i)

bx+ay=2ab

bx+a(b)=2ab

bx=2ab-ab

bx=ab

x=ab/b

x=a

So, x=a and y=b