Solve the following system of equations:1/(5x) + 1/(6y) = 12; 1/(3x)

1.	Solve the following system of equations:1/(5x) + 1/(6y) = 12; 1/(3x) – 3/(7y) = 8
Answer» Let 1/x = u and 1/y = v So, the given equations becomes u/5 + v/6 = 12………(i) u/3 – 3v/7 = 8………(ii) Taking LCM for both equations, we get 6u + 5v = 360………(iii) 7u – 9v = 168……….(iv) Subtracting (iii) from (iv) 7u – 9v – (6u + 5v) = 168 – 360 ⇒ u – 14v = -192 ⇒ u = (14v – 192)………. (v) Using (v) in equation (iii), we get 6(14v – 192) + 5v = 360 ⇒ 84v -1152 + 5v = 360 ⇒ 89v = 1512 ⇒ v = 1512/89 ⇒ y = 1/v = \(\frac{89}{1512}\) Now, substituting v in equation (v), we find u u = 14 x (1512/89) – 192 ⇒ u = \(\frac{4080}{89}\) ⇒ x = 1/u = \(\frac{89}{4080}\) Hence, the solution for the given system of equations is x = \(\frac{89}{4080}\) and y = \(\frac{89}{1512}\).

Solve the following system of equations:1/(5x) + 1/(6y) = 12; 1/(3x) – 3/(7y) = 8

Answer»

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

So, the given equations becomes

u/5 + v/6 = 12………(i)

u/3 – 3v/7 = 8………(ii)

Taking LCM for both equations, we get

6u + 5v = 360………(iii)

7u – 9v = 168……….(iv)

Subtracting (iii) from (iv)

7u – 9v – (6u + 5v) = 168 – 360

⇒ u – 14v = -192

⇒ u = (14v – 192)………. (v)

Using (v) in equation (iii), we get

6(14v – 192) + 5v = 360

⇒ 84v -1152 + 5v = 360

⇒ 89v = 1512

⇒ v = 1512/89

⇒ y = 1/v = \(\frac{89}{1512}\)

Now, substituting v in equation (v), we find u

u = 14 x (1512/89) – 192

⇒ u = \(\frac{4080}{89}\)

⇒ x = 1/u = \(\frac{89}{4080}\)

Hence, the solution for the given system of equations is x = \(\frac{89}{4080}\) and y = \(\frac{89}{1512}\).