Question

Solve
the following simultaneous equation 2/x +6/y =13 ; 3/x +4/y = 12​

Answer 1

Answer:

x=1/2 and y=2/3

Step-by-step explanation:

The above attachment contains the procedure.

Answer 2

Answer

$\sf \dashrightarrow \dfrac{2}{x} + \dfrac{6}{y} = 13 \: \: --- (i)$

$\sf \dashrightarrow \dfrac{3}{x} + \dfrac{4}{y} = 12 \: \: --- (ii)$

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

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

So, the equations become

$\sf \dashrightarrow 2u + 6v = 13$

$\sf \dashrightarrow 3u + 4v = 12$

By first equation,

$\sf \dashrightarrow 2u = 13 - 6v$

$\sf \dashrightarrow u = \dfrac{13 - 6v}{2}$

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

$\sf \dashrightarrow 3u + 4v = 12$

$\sf \dashrightarrow 3 \bigg( \dfrac{13 - 6v}{2} \bigg) + 4v = 12$

$\sf \dashrightarrow \dfrac{39 - 18v}{2} + 4v = 12$

$\sf \dashrightarrow \dfrac{39 - 18v + 8v}{2} = 12$

$\sf \dashrightarrow \dfrac{39 - 10v}{2} = 12$

$\sf \dashrightarrow 39 - 10v = 12 \times 2$

$\sf \dashrightarrow 39 - 10v = 24$

$\sf \dashrightarrow -10v = 24 - 39$

$\sf \dashrightarrow -10v = -15$

$\sf \dashrightarrow v = \dfrac{-15}{-10}$

$\sf \dashrightarrow v = \dfrac{3}{2}$

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

$\sf \dashrightarrow 2u + 6v = 13$

$\sf \dashrightarrow 2u + 6 \bigg( \dfrac{3}{2} \bigg) = 13$

$\sf \dashrightarrow 2u + \dfrac{18}{2} = 13$

$\sf \dashrightarrow 2u + 9 = 13$

$\sf \dashrightarrow 2u = 13 - 9$

$\sf \dashrightarrow 2u = 4$

$\sf \dashrightarrow u = \dfrac{4}{2}$

$\sf \dashrightarrow u = 2$

We know that,

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

$\sf \dashrightarrow \dfrac{1}{x} = 2$

$\sf \dashrightarrow 2x = 1$

$\sf \dashrightarrow x = \dfrac{1}{2}$

We also know that,

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

$\sf \dashrightarrow \dfrac{1}{y} = \dfrac{3}{2}$

$\sf \dashrightarrow 3y = 2$

$\sf \dashrightarrow y = \dfrac{2}{3}$

Hence, the value of x and y are 1/2 and 2/3 respectively.