Math, asked by ujjwalkharkwal11, 1 year ago

solve 2÷3(x-y) + 5÷2y = 2 and 1÷2(x-y) - 1÷y by reduction method

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Answered by pratik40

$hi...$

$\frac{2}{3(x - y)} + \frac{5}{2y} = 2$

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

Let
$\frac{1}{x - y} \: \: be \: \: a$
&
$\frac{1}{y } \: \: \: b e \: \: \: b$
So we get..

$\frac{2}{3} a + \frac{5}{2} b = 2 \: \: \:$

$\frac{4a + 15b}{2 \times 3} = 2$

$\frac{4a + 15b}{6} = 2$

$4a + 15b = 2 \times 6$

$4a + 15b = 12 \: \: ............(1)$
&
$\frac{1}{2} a - b = - 1 \: \:$
[Multiplying equation by 2]

$a - 2b = - 2 \: \: ...............(2)$

[ Multiplying equation (2) by 4 ]

$4a - 8b = - 8\: \: ..............(3)$
[Subtracting equation no. (3) from (1)]

$4a + 15b = 12$
$4a - 8b = - 8$
__________________
23b = 20

b = 20 / 23

Substitute in equation no. (2)

$a - 2b = - 2$

$a - 2( \frac{20}{23} ) = - 2$

$a - \frac{40}{23} = - 2$

$a = - 2 + \frac{40}{23}$

$a = \frac{ - 46 +40}{2 3}$

$a = \frac{ - 6}{23}$

Resubstituting ,

$\frac{1}{x - y} = a$

$\frac{1}{x - y} = \frac{ - 6}{23}$

$23 = - 6(x - y)$

$23 = - 6x + 6y$

$6x - 6y = - 23..........(4)$
And ..

$\frac{1}{y} = b$

$\frac{1}{y} = \frac{20}{23}$

${y} = \frac{23}{20}$

Substitute in equation (4)

$6x - 6y = - 23$

$6x - 6( \frac{23}{20} ) = - 23$

$6x - 3( \frac{23}{10} ) = - 23$

$6x - \frac{69}{10} = - 23$

$6x = - 23 + \frac{69}{10}$

$6x = \frac{ - 230 + 69}{10} [/text]<br /><br />[tex]6x = \frac{ - 161}{10}$

$x = \frac{ - 161}{10} \times \frac{1}{6}$

[text] = \frac{ - 161}{60} [/text]
___________________________
$x = \frac{ - 161}{60} \: . \: y = \frac{ 23}{20}$
$hope \: this \: helps...$

ujjwalkharkwal11: thank you

ujjwalkharkwal11: here is no option of brainiest answer

ujjwalkharkwal11: how should I make it

Answered by Anonymous

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