Q.

Solve the following system of linear equations.


 ax+by=a-b and bx-ay=a+b.


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a

x=a,y=-b

b

x=1,y=-1

c

x=-1,y=1

d

x=1a,y=-1b  

answer is B.

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Detailed Solution

Given the system of linear equation is,
 ax+by=a-b ............ (1)
bx-ay=a+b  .............. (2) .
Multiply equation (1) with a we get,,
a(ax+by)=a(a-b)
 a2x+aby=a2-ab  ................. (3) .
Multiply equation (2) with b we get,
b(bx-ay)=b(a+b)
 b2x-aby=ab+b2  ................. (4) .
Adding equation (3) and (4) we get,
 (a2x+ab)+(b2x-aby)=(a2+b2)+( ab+b2)
(a2+b2)x=(a2+b2)
x=1 (Since a2+b2 0)
Now substituting x=1 in equation (1) we get,
 a(1)+by=a-b a+by=a-b
by=-b y=-bb
y=-1 So the correct option  2.
 
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