Question

Solve the following pair of equation
1/3x + y + 1/3x - y = 3/4 , 1/2(3x + y) - 1/2(x-y) = -1/8

Answer 1

1

+

3x−y

1

=

4

3

Let 1/3x + y = a , and 1/3x - y = b ,

a + b = 3/4 -----------------> (1)

4a + 4b = 3 -------------> (1)

also ,

\frac{1}{2 ( 3x + y)} - \frac{1}{2(3x - y)} = -1/8

2(3x+y)

1

−

2(3x−y)

1

=−1/8

a/2 - b/2 = -1/8

(a - b)/2 = -1/8

a - b = -1/4

4a - 4b = -1 ---------------------------> (2)

Adding equations (1) and (2) :-

4a + 4b = 3

4a - 4b = -1

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

8a = 2

a = 2/8

a = 1/4

4a - 4b = -1

4*1/4 - 4b = -1

1 - 4b = -1

4b = 1 + 1

4b = 2

b = 2/4

b = 1/2

1/3x + y = a

1/3x + y = 1/4

3x + y = 4 -----------------> (3)

1/3x - y = b

1/3x - y = 1/2

3x - y = 2 -----------------> (2)

Adding equations (3) and (4) :-

3x + y = 4

3x - y = 2

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

6x = 6

x = 1

3x + y = 4

3*1 + y = 4

y = 4 - 3 = 1

Hence,

x = 1 , y = 1

Answer 2

Answer:

       1           +          1           =   3

    3x+y                   3x-y              4

Let 1/3x + y = a , and 1/3x - y = b ,

a + b = 3/4       -----------------> (1)

4a + 4b = 3                   -------------> (1)

also ,

       1           +          1           =   -1  

  2( 3x+y)              2(3x-y)            8

a/2 - b/2 = -1/8

(a - b)/2 = -1/8

a - b = -1/4

4a - 4b = -1                   ---------------------------> (2)

Adding equations (1) and (2) :-

4a + 4b = 3

4a - 4b = -1

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

8a = 2

a = 2/8

a = 1/4

4a - 4b = -1

4*1/4 - 4b = -1

1 - 4b = -1

4b = 1 + 1

4b = 2

b = 2/4

b = 1/2

1/3x + y = a  

1/3x + y = 1/4

3x + y = 4         -----------------> (3)

1/3x - y = b

1/3x - y = 1/2

3x - y = 2                 -----------------> (2)

Adding equations (3) and (4) :-

3x + y = 4

3x - y = 2

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

6x = 6

x = 1

3x + y = 4

3*1 + y = 4

y = 4 - 3 = 1

Hence,

x = 1 , y = 1