Solve the following system of equations:2/x + 3/y = 9/xy 4/x + 9/y =

1.	Solve the following system of equations:2/x + 3/y = 9/xy 4/x + 9/y = 21/xy
Answer» Taking LCM for both the given equations, we have (2y + 3x)/ xy = 9/xy ⇒ 3x + 2y = 9………. (i) (4y + 9x)/ xy = 21/xy ⇒ 9x + 4y = 21………(ii) Performing (ii) – (i) x 2 ⇒ 9x + 4y – 2(3x + 2y) = 21 – (9×2) ⇒ 3x = 3 ⇒ x = 1 Using x = 1 in (i), we find y 3(1) + 2y = 9 ⇒ y = \(\frac{6}{2}\) ⇒ y = 3 Thus, the solution for the given set of equations is x = 1 and y = 3.

Solve the following system of equations:2/x + 3/y = 9/xy 4/x + 9/y = 21/xy

Answer»

Taking LCM for both the given equations, we have

(2y + 3x)/ xy = 9/xy

⇒ 3x + 2y = 9………. (i)

(4y + 9x)/ xy = 21/xy

⇒ 9x + 4y = 21………(ii)

Performing (ii) – (i) x 2

⇒ 9x + 4y – 2(3x + 2y) = 21 – (9×2)

⇒ 3x = 3

⇒ x = 1

Using x = 1 in (i), we find y

3(1) + 2y = 9

⇒ y = \(\frac{6}{2}\)

⇒ y = 3

Thus, the solution for the given set of equations is x = 1 and y = 3.