Solve the following system of equations:15/u + 2/v = 17; 1/u + 1/v =

1.	Solve the following system of equations:15/u + 2/v = 17; 1/u + 1/v = 36/5
Answer» Let 1/x = u and 1/y = v So, the given equations becomes 15x + 2y = 17 ……………(i) x + y = \(\frac{36}{5}\)………………(ii) From equation (i) we get, 2y = 17 – 15x y = \(\frac{(17 − 15x)}{ 2}\) …………(iii) Substituting (iii) in equation (ii) we get, x + \(\frac{(17 − 15x)}{2}\) = \(\frac{36}{5}\) 2x + 17 – 15x = (36 x 2)/ 5 [after taking LCM] -13x = \(\frac{72}{5}\) – 17 -13x = -\(\frac{13}{5}\) ⇒ x = \(\frac{1}{5}\) ⇒ u = \(\frac{1}{x}\) = 5 Putting x = \(\frac{1}{5}\) in equation (ii) , we get \(\frac{1}{5}\) + y = \(\frac{36}{5}\) ⇒ y = 7 ⇒ v = \(\frac{1}{y}\) = \(\frac{1}{7}\) The solution of the pair of equations given are u = 5 and v = \(\frac{1}{7}\) respectively.

Solve the following system of equations:15/u + 2/v = 17; 1/u + 1/v = 36/5

Answer»

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

So, the given equations becomes

15x + 2y = 17 ……………(i)

x + y = \(\frac{36}{5}\)………………(ii)

From equation (i) we get,

2y = 17 – 15x

y = \(\frac{(17 − 15x)}{ 2}\) …………(iii)

Substituting (iii) in equation (ii) we get,

x + \(\frac{(17 − 15x)}{2}\) = \(\frac{36}{5}\)

2x + 17 – 15x = (36 x 2)/ 5 [after taking LCM]

-13x = \(\frac{72}{5}\) – 17

-13x = -\(\frac{13}{5}\)

⇒ x = \(\frac{1}{5}\)

⇒ u = \(\frac{1}{x}\) = 5

Putting x = \(\frac{1}{5}\) in equation (ii) , we get

\(\frac{1}{5}\) + y = \(\frac{36}{5}\)

⇒ y = 7

⇒ v = \(\frac{1}{y}\) = \(\frac{1}{7}\)

The solution of the pair of equations given are u = 5 and v = \(\frac{1}{7}\) respectively.