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Question

Solve: ax+by=c,bx+ay=1+c

A
x=abcba2b2,y=acbc+aa2ab2
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B
x=acbcba2b2,y=acc+baa2b2
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C
x=abcba2b2,y=bcc+baa2c2
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D
None of these
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Solution

The correct option is D None of these
ax+by=c ....(1)
bx+ay=1+c ....(2)
Adding (1) and (2), we get
(a+b)x+(a+b)y=2c+1
x+y=2c+1a+b ....(3)
Subtracting (2) and (1), we get
(ab)x(ab)y=1
xy=1ab .....(4)
Adding (3) and (4), we get
2x=2c+1a+b+1ab=2ac2bc+ababa2b2
2x=2ac2bc2ba2b2
x=acbcba2b2
Subtracting (4) from (3) we get
2y=2c+1a+b++1ab=2ac2bc+ab+a+ba2b2
2y=2ac2bc+2aa2b2
y=ac+bc+aa2b2
Hence, x=acbcba2b2,y=acbc+aa2b2

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