Solve the following system of equations:2/x + 3/y = 13; 5/x – 4/y =

1.	Solve the following system of equations:2/x + 3/y = 13; 5/x – 4/y = -2
Answer» Let 1/x = u and 1/y = v So, the given equations becomes 2u + 3v = 13…………(i) 5u – 4v = -2 …………(ii) Adding equation (i) and (ii) we get, 2u + 3v + 5u – 4v = 13 – 2 ⇒ 7u – v = 11 ⇒ v = 7u – 11…….. (iii) Using (iii) in (i), we get 2u + 3(7u – 11) = 13 ⇒ 2u + 21u – 33 = 13 ⇒ 23u = 46 ⇒ u = 2 Substituting u = 2 in (iii), we find v v = 7(2) – 11 ⇒ v = 3 Hence, x = 1/u = 1/2 and, y = 1/v = 1/3.

Solve the following system of equations:2/x + 3/y = 13; 5/x – 4/y = -2

Answer»

Let 1/x = u and 1/y = v

So, the given equations becomes

2u + 3v = 13…………(i)

5u – 4v = -2 …………(ii)

Adding equation (i) and (ii) we get,

2u + 3v + 5u – 4v = 13 – 2

⇒ 7u – v = 11

⇒ v = 7u – 11…….. (iii)

Using (iii) in (i), we get

2u + 3(7u – 11) = 13

⇒ 2u + 21u – 33 = 13

⇒ 23u = 46

⇒ u = 2

Substituting u = 2 in (iii), we find v

v = 7(2) – 11

⇒ v = 3

Hence, x = 1/u = 1/2 and, y = 1/v = 1/3.