Question

2 / x + 1 / y = 10 and 3 / x + 2 / y = 1 solve simultaneous equation

Answer 1

Answer

$\sf \dashrightarrow \dfrac{2}{x} + \dfrac{1}{y} = 10 \: \: --- (i)$

$\sf \dashrightarrow \dfrac{3}{x} + \dfrac{2}{y} = 1 \: \: --- (ii)$

Let $\sf \dfrac{1}{x}$ be u.

Let $\sf \dfrac{1}{y}$ be v.

So, the equations become

$\sf \dashrightarrow 2u + 1v = 10$

$\sf \dashrightarrow 3u + 2v = 1$

By first equation,

$\sf \dashrightarrow 2u + 1v = 10$

$\sf \dashrightarrow 2u = 10 - 1v$

$\sf \dashrightarrow u = \dfrac{10 - 1v}{2}$

Now, let's find the value of v by second equation.

$\sf \dashrightarrow 3u + 2v = 1$

$\sf \dashrightarrow 3 \bigg( \dfrac{10 - 1v}{2} \bigg) + 2v = 1$

$\sf \dashrightarrow \dfrac{30 - 2v}{2} + 2v = 1$

$\sf \dashrightarrow \dfrac{30 - 2v + 4v}{2} = 1$

$\sf \dashrightarrow \dfrac{30 + 2v}{2} = 1$

$\sf \dashrightarrow 30 + 2v = 2$

$\sf \dashrightarrow 2v = 2 - 30$

$\sf \dashrightarrow 2v = -28$

$\sf \dashrightarrow v = \dfrac{-28}{2}$

$\sf \dashrightarrow v = -14$

Now, let's find the value of u by first equation.

$\sf \dashrightarrow 2u + 1v = 10$

$\sf \dashrightarrow 2u + 1(-14) = 10$

$\sf \dashrightarrow 2u - 14 = 10$

$\sf \dashrightarrow 2u - 14 = 30$

$\sf \dashrightarrow 2u = 30 + 14$

$\sf \dashrightarrow 2u = 44$

$\sf \dashrightarrow u = \dfrac{44}{2}$

$\sf \dashrightarrow u = 22$

We know that,

$\sf \dashrightarrow \dfrac{1}{x} = u$

$\sf \dashrightarrow \dfrac{1}{x} = 22$

$\sf \dashrightarrow 22x = 1$

$\sf \dashrightarrow x = \dfrac{1}{22}$

We also know that,

$\sf \dashrightarrow \dfrac{1}{y} = v$

$\sf \dashrightarrow \dfrac{1}{y} = -14$

$\sf \dashrightarrow -14y = 1$

$\sf \dashrightarrow y = \dfrac{1}{-14}$

$\sf \dashrightarrow y = \dfrac{-1}{14}$

Hence, the values of x and y are 1/22 and -1/14 respectively.