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)
.
0+ (a3 - a2 b)y = a2b3-a3b2
So,
(a3 - a2 b)y = a2b3-a3b2
a2 ( a – b)y = -a2b2 ( a – b)
y = - b2
Substitute the value in (2)
b2x-a2y=2a2b2
b2x-a2(-b2) =2a2b2
b2x + a2b2 =2a2b2
( x + a2) = 2 a2
x = a2
The value x = a2 and y = -b2
.