Question

1/3x+y +1/3x-y=3/4 eq no. 1
1/2(3x+y)-1/2(3x-y)=-1/8 eq no. 2​

Answer 1

Answer:

take 1/(3x+y) = a

and 1/(3x-y) = b

now ,

equation 1

a + b = 3/4

4a + 4b = 3 -------equation 3

and equation 2

a/2 - b/2 = 1/8

(a-b)/2 = 1/8

a-b = 1/4

4a - 4b = 1 ---------equation 4

solve

4a + 4b = 3

4a - 4b = 1

------------------

8a - 0 = 4

a = 4/8

a= 1/2

put value of a in equation 4 or 3 to get the value of b

4a - 4b = 1

4(1/2) - 4b =1

2 - 4b = 1

4b = 1

b = 1/4

now we had taken 1/(3x+y) = a

1/(3x+y) = aand 1/(3x-y) = b

1/(3x+y) = a

1/(3x+y) = 1/2

by cross multiplication

we get a equation

3x + y = 2 ---------equation 5

and

1/(3x-y) = b

1/(3x-y) = 1/4

by cross multiplication

we get a equation

3x - y = 4 ---------equation 6

now solve equations 5 and 6 to get the value of x and y

3x + y = 2

3x - y = 4

---------------

6x - 0 = 6

6x = 6

x = 1

put the value of x in equations 5 and 6 to get the value of y

3x + y = 2

3(1) + y = 2

y= 2 - 3

y = -1