Question

solve the following pairs of equations by reducing them to a pair of linear equations .1) 1/3x+y+1/3x-y=3/4and 1/2(3x+y)-1/2(3x-y)=-1/8

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Answer 1

Answer:

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

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

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

also ,

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

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