If \(\frac{2}x+\frac{3}y= -\frac{9}{xy}\) and \(\frac{4}x+\frac{9}y

1.	If \(\frac{2}x+\frac{3}y= -\frac{9}{xy}\) and \(\frac{4}x+\frac{9}y= \frac{21}{xy}\), find the values of x and y.
Answer» The given pair of equation is 2/x + 3/y = 9/xy ………(i) 4/x + 9/y = 21/xy ………(ii) Multiplying (i) and (ii) by xy, we have 3x + 2y = 9 ……….(iii) 9x + 4y = 21 ………(iv) Now, multiplying (iii) by 2 and subtracting from (iv), we get 9x – 6x = 21 – 18 ⇒ x = 3/3 = 1 Putting x = 1 in (iii), we have 3 × 1 + 2y = 9 ⇒ y = 9−3/2 = 3 Hence, x = 1 and y = 3.

If \(\frac{2}x+\frac{3}y= -\frac{9}{xy}\) and \(\frac{4}x+\frac{9}y= \frac{21}{xy}\), find the values of x and y.

Answer»

The given pair of equation is

2/x + 3/y = 9/xy ………(i)

4/x + 9/y = 21/xy ………(ii)

Multiplying (i) and (ii) by xy, we have

3x + 2y = 9 ……….(iii)

9x + 4y = 21 ………(iv)

Now, multiplying (iii) by 2 and subtracting from (iv), we get

9x – 6x = 21 – 18 ⇒ x = 3/3 = 1

Putting x = 1 in (iii), we have

3 × 1 + 2y = 9 ⇒ y = 9−3/2 = 3

Hence, x = 1 and y = 3.