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Answer» Here is your solution :
⇒ ax + by = C -------- ( 1 )
⇒ bx + AY = 1 + c -------- ( 2 )
Multiply the eq'n( 1 ) by ' a ',
⇒ a( ax + by ) = AC
⇒ a²x + aby = ac ------ ( 3 )
Multiply the eq'n ( 2 ) by 'b',
⇒b( bx + ay ) = b( 1 + c )
⇒ b²x + aby = b + bc ------ ( 4 )
Subtract the eq'n ( 4 ) from eq'n ( 3 ),
⇒ a²x + aby - b²x - aby = ac - b - bc
⇒ a²x - b²x = ac - bc - b
⇒ x( a² - b² ) = ac - bc - b
•°• x = [ ac - bc - b ] / ( a² - b² )
Substitute the value of ' x ' in eq'n( 1 ),
⇒ ax + by = c
⇒ a[ ( ac - bc - b ) / ( a² - b² ) ] + by = c
⇒ [ ( a²c - ABC - ab ) / ( a² - b² ) ] + by = c
⇒ by = c - [ ( a²c - abc - ab ) / ( a² - b² ) ]
⇒ by = [ a²c - b²c - a²c + abc + ab ] / ( a² - b² )
⇒ by = ( abc + ab - b²c ) / ( a² - b² )
⇒ by = b( ac + a - bc ) / ( a² - b² )
⇒ y = [ b( ac + a - bc ) ] / [ b( a² - b² ) ]
•°• y = ( ac + a - bc ) / ( a² - b² )
Hence,
⇒ x = ( ac - bc - b ) / ( a² - b² )
⇒ y = ( ac - bc + a ) / ( a² - b² )
HOPE it helps !!
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