Question

find the values of x and y
14/2x+y + 3/2x-y=5

3/2x+y - 4/2x-y=-25/7

Answer 1

Heya !!!



14/ 2X + Y + 3/2X - Y = 5 -------(1)



3/2 X + Y - 4/2X - Y = -25/7 ------(2)



Let , 1/2X + Y = U and 1/2X - Y = V.



Putting 1/2X + Y = U and 1/2X-Y = V in equation (1) and (2). Then equation (1) and (2) becomes,



14U + 3V = 5 -------(3)



And,



3U - 4V = -25/7



7( 3U - 4V) = -25



21U - 28V = -25 --------(4)



From equation (3) we get,

14U + 3V = 5



14U = 5 -3V



U = 5-3V/14 -----------(5)


Putting the value of U in equation (4) we get,


21U - 28V = -25



21 × ( 5 - 3V/14) - 28V = -25




3 ( 5-3V/2) - 28V = -25




15 - 9V/2 - 28V = -25




15 - 9V - 56V/2 = -25




-65V + 15 = -50



-65V = -50 -15



-65V = -65



V = -65/-65 = 1


Putting the value of V in equation (5)



U = 5-3V/14 => 5 - 3 × 1/14 = 5 -3/14



U = 2/14 = 1/7



Now,



1/2X + Y = U



1/2X + Y = 1/7



7 = 2X + Y



2X + Y = 7 ----------(6)



And,



1/2X - Y = V



1/2X - Y = 1



2X - Y = 1 -----------(7)



From equation (6) we get,


2X + Y = 7



2X = 7 -Y


X = 7 -Y/2 --------(8)



Putting the value of X in equation (7)


2X - Y = 1



7-Y/2 - Y = 1



7 - Y - 2Y/2 = 1




-3Y + 7 = 1



-3Y = 1-7




-3Y = -6



Y = -6/-3 = 2




Putting the value of Y in equation (8)



X = 7-Y/2 => 7 - 2/2




X = 5/2.






Hence,



X = 5/2 and Y = 2.




HOPE IT WILL HELP YOU..... :-)