Question
Wed July 18, 2012 By:

# Solve for x and y:

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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