Question

hello guys pls solve this equation ​

Answer 1

Answer:

Given:

2 Equations as follows :

• 3/x + 8/y = -1
• 1/x - 2/y = 2

To find :

Value of x and y

Concept:

Take 1/x = a and 1/y = b

Calculation:

∴ 3a + 8b = -1 ..........eq (1)

∴ a - 2b = 2 ..........eq(2)

Now multiply eq(2) with 3 and subtract the 2 Equations :

3a + 8b = -1

3a - 6b = 6

(-) (+) (-)

0 + 14b = -7

=> b = -½

=> 1/y = -½

=> y = -2

Now putting value of b in eq (2)

∴ a - 2b = 2

=> a + 1 = 2

=> a = 1

=> 1/x = 1

=> x = 1

So final answer :

• x = 1
• y = -2

Answer 2

Given,

$\frac{3}{x} + \frac{8}{y} = ( - 1) - - - 1st \: equation \\ \frac{1}{x} - \frac{2}{y} = 2 - - - 2nd \: equation\\ \\ let \: \: (\frac{1}{x} = u) \: and \: ( \frac{1}{y} = v) \\ \\ then$

1st equation can be written as,

$3u + 8v = ( - 1)$

and 2nd equation can be written as,

$u - 2v = 2 \\ = 3 \times (u - 2v) = 3 \times 2 (\: multiplying 3\: on \: both \: side) \\ = 3u - 6v = 6$

subtracting equation 2 from equation 1 we get,

$(3u + 8v) - (3u - 6v) = ( - 1) - (6) \\ = 3u + 8v - 3u + 6v = - 1 - 6 \\ = 14v = ( - 7) \\ = v = \frac{ - 1}{2}$

but we know,

$\frac{1}{y} = v \\ thus \\ \frac{ - 1}{2} = v = \frac{1}{y} \\ y = ( - 2)$

putting the value,

$y= {2} \: in \: equation \: 2 \: we \: get$

$\frac{1}{x} - \frac{2}{ - 2} = 2 \\ \frac{1}{x} = 2 + \frac{2}{-2} \\ \frac{1}{x} = 2-1\\ \frac{1}{x} = 1 \\ x = 1$

$thus \: x =1 \: and \: \: y = ( - 2)$