Solve for x and y ,
` 37x + 43 y = 123, 43 x + 37 y = 117`

Options

A. `x=1 ,y=1`
B. `x=2 , y=1`
C. `x=1, y=2`
D. `x=2 ,y=2`

Answer

C

Explanation

The given equations are
` 37 x + 43 y = 123" " `… (i)
` 43 x + 37y = 117 " " `.. . (ii)
Clearly , the coefficients of x and y in one equation are interchanged in the other.
Adding (i) and (ii), we get
` ( 37 + 43 )x + ( 43 + 37) y = ( 123 + 117) `
`rArr 80 x + 80 y = 240`
` rArr 80 ( x + y ) = 240 `
` rArr x + y = ( 240 )/(80) rArr x + y = 3 " " `... (iii)
Subtracting (i) from (ii), we get
` 6x - 6y = - 6 `
` rArr 6 ( x- y ) = - 6 rArr x - y = - 1 " " `... (iv)
Adding (iii) and (iv), we get ` 2 x = 2 rArr x = 1 `
Subtracting (iv) from (iii) , we get ` 2y = 4 rArr y = 2`
Hence, ` x = 1 and y = 2`.