ax + by = c + 1
bx + ay = c
find the value of x and y
Answers
Answer:
x = ( ac + a - bc ) / ( a^2 - b^2 )
y = ( ac - bc - b ) / ( a^2 - b^2 )
Step-by-step explanation:
Given,
ax + by = c + 1 ...( 1 )
bx + ay = c ...( 2 )
Multiplying both sides of ( 1 ) by b :
= > [ ax + by = c + 1 ] × b
= > abx + b^2 y = cb + b ...( 3 )
Multiplying both sides of ( 2 ) by a :
= > [ bx + ay = c ] × a
= > abx + a^2 y = ac ...( 4 )
Subtracting ( 3 ) from ( 4 ) :
= > ( abx + a^2 y ) - ( abx + b^2 y ) = ac - ( cb + b )
= > abx + a^2 y - abx - b^2 y = ac - cb - b
= > a^2 y - b^2 y = ac - bc - b
= > y( a^2 - b^2 ) = ( ac - bc - b )
= > y = ( ac - bc - b ) / ( a^2 - b^2 )
Substituting the value of y in ( 2 ) :
= > bx + a( ac - bc - b ) / ( a^2 - b^2 ) = c
= > bx = c - a( ac - bc - b ) / ( a^2 - b^2 )
= > x = { c - a( ac - bc - b ) / ( a^2 - b^2 ) } / b
= > x = { a^2c - b^2c - a^2c + abc + ab } / b( a^2 - b^2 )
= > x = ( abc + ab - b^2c ) / b( a^2 - b^2 )
= > x = ( ac + a - bc ) / ( a^2 - b^2 )
Answer:
Hope it helps you friend.
