Q. 274.3( 16 Votes )

# Solve for x and y:

Answer :

We have

and

Lets simplify these equations. Assuming p = 1/(x + y) and q = 1/(x – y),

5p – 2q = - 1 …(i)

Also,

⇒ 15p + 7q = 10 …(ii)

To solve these equations, we need to make one of the variables (in both the equations) have same coefficient.

Lets multiply eq.(i) by 3, so that variable p in both the equations have same coefficient.

Recalling equations (i) & (ii),

5p – 2q = - 1 [×3

15p + 7q = 10

⇒ - 13q = - 13

⇒ q = 1

Substitute q = 1 in eq.(i)/eq.(ii), as per convenience of solving.

Thus, substituting in eq.(i), we get

5p – 2(1) = - 1

⇒ 5p – 2 = - 1

⇒ 5p = 2 – 1 = 1

⇒ p = 1/5

Thus, p = 1/5 and q = 1

As p = 1/(x + y),

⇒

⇒ x + y = 5 …(iii)

And q = 1/(x – y)

⇒

⇒ x – y = 1 …(iv)

Adding equations (iii) and (iv) to obtain x and y,

(x + y) + (x – y) = 5 + 1

⇒ 2x = 6

⇒ x = 3

Putting the value of x in equation (iii), we get

3 + y = 5

⇒ y = 2

Hence, we have x = 3 and y = 2

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