Question
Wed July 18, 2012 By:
 

Solve for x and y:

Expert Reply
Fri July 20, 2012
Answer : Given : 7/ ( 4x + 3y ) +4 /(4-3y) = 5/4
 14/ ( 4x + 3y ) + 18 /(4-3y) = 3/2
 
To find : the values of x and y 
 
Let 1/ ( 4x+ 3y) = p and  1/ ( 4x - 3y) = q
 
Therefore the quations become as follows :
=> 7p + 4q = 5/4 ........................(1)
and 14 p+ 18 q = 3/2.................(2)
 
=> 7p + 4q = 5/4
 7 p+ 9q = 3/4     
subtracting the above two equations we get , 
-5q= 1/2 
=> q = - 1/10 
 
putting the value of q in eq (1) , we get 
=>7 p + 4 ( - 1/10) = 5/4
 =>7p = (5/4) + ( 2/5 )
 
=> p = 33/140 
 
Since we know that 
 1/(4x+ 3y) = p and  1/ ( 4x - 3y) = q
=> 4x + 3y = 140/33 ............................(3)
and 4x-3y= -10.....................................(4)
 
Adding eq (3) and eq(4) , we get 
8x = -190 /33
=> x = - 190 /(33* 4)
=> x= -95 / 132
 
putting the value of x in eq (3), we get
=>4(-95/132) + 3y = 140 /33
=> -95 / 33 + 3y = 140/33
=> 3y = (140+95) /33
=> 3y = 235 /33
=> y = 235 / 99
 
Answer : x= -95/132  and y = 235/99
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