solve the system for x and y

b2x/a-a2y/b=ab(a+b) and b2x-a2y=2a2b2


Dear Student,

Solving the given equations by ELIMINATION METHOD:

b2x/a-a2y/b=ab(a+b)  ----------------(1)
 b2x-a2y=2a2b2  ----------------(2)

Multiply the equation (1) by “ ab”, you get :
 b3x-  a3y = a2b2 (a+b) 
b3x-  a3y = a3b2 + a2b3  ---------------(3)

Consider (2) and (3)
Now multiply (2) by “b”
b3x-a2 by=2a2b3

Subtract the above equation with (3)
b3x-a2 by=2a2b3
(-)b3x -(+) a3y =(-)a2b3 +(-)a3b2  
  . 
0+ (a3 - a2 b)y = a2b3-a3b2 

So,
(a3 - a2 b)y = a2b3-a3b2 
a2 ( a – b)y = -a2b2 ( a – b)
a2 y = - a2b2
y = - b2 

Substitute the value in (2)
b2x-a2y=2a2b2
b2x-a2(-b2) =2a2b2
b2x + a2b2 =2a2b2
b2( x + a2) =  2 a2 b2
( x + a2) =  2 a2
x = a2

The value x = a2 and y = -b2

 .

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