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Solve for x & y: a x+b y=a-b ,\ \ \ \ b...

Solve for `x` & `y`:
`a x+b y=a-b ,\ \ \ \ b x-a y=a+b`

A

2,3

B

1,-1

C

1,2

D

a,b

Text Solution

Verified by Experts

The correct Answer is:
B
The given equations may be written as
` a x + by = a - b " " `… (i)
` bx - ay = a + b " " `… (ii)
Multiplying (i) by a and (ii) by b and adding the results, we get
`(a ^(2) + b ^(2)) x = (a ^(2) + b ^(2)) rArr x = 1 `
Putting ` x = 1 ` in (i) , we get
` ( a xx 1 ) + by = a- b `
` rArr a + by = a - b `
` rArr by = - b rArr y = (-b)/(b) = - 1 `
Hence, ` x = 1 and y = - 1`.
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