Question

Solve the following for x and y by using method of elimination.

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

Kindly solve on paper and than send as it's a lengthy question.

Answer 1

HELLO DEAR,



(a + 2b)x + (2a - b) = 2-----------( 1 )
(a - 2b)x + (2a + b) = 3-----------( 2 )



adding-------( 1 ) & -------( 2 )


we get,

(a + 2b)x + (2a - b)y = 2
(a - 2b)x + (2a + b)y = 3
————————————-
x(a + 2b + a - 2b) + y(2a - b + 2a + b) = 5

⇒2ax + 4ay = 5---------( 3 )




Now,

subtracting-------( 1 ) & -------( 2 )


(a + 2b)x + (2a - b)y = 2
(a - 2b)x + (2a + b)y = 3
(-)______(-)_______(-)
————————————-
x[(a + 2b) - (a - 2b)] + y[(2a - b) - (2a + b) = -1


⇒x(a + 2b - a + 2b) + y(2a - b - 2a - b) = -1


⇒4bx - 2by = - 1----------( 4 )



From-------( 3 ) & ----------( 4 )
multiply by "(2b)" in ---( 3 ) , by "(a) in ----( 4 )




4abx + 8aby = 10b
4abx - 2aby = -a
(-)____(+)____(+)
——————————
10aby = (10b + a)


Y = (10b + a)/10ab [ put in -----( 3 ) ]


we get,


2ax + 4ay = 5

⇒2ax + 4a(10b + a)/10ab = 5

⇒2ax + (20b + 2a)/5b = 5

⇒[ 10abx + 20b + 2a ] / 5b = 5

⇒10abx + 20b + 2a = 25b

⇒10abx = (25b - 20b - 2a)

⇒10abx = (5b - 2a)

⇒x = (5b - 2a)/10ab , y = (10b + a)/10ab





I HOPE ITS HELP YOU DEAR,
THANKS

Answer 2

Hope it helps you ...........