Question

find the value of x and y using add and subtract method ...
please answer​ with steps​

Answer 1

Step-by-step explanation:

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Answer 2

$\large\underline{\sf{Solution-}}$

Given pair of linear equations are

$\rm :\longmapsto\:\dfrac{7}{2x + 1} + \dfrac{13}{y + 2} = 27 - - (1)$

and

$\rm :\longmapsto\:\dfrac{13}{2x + 1} + \dfrac{7}{y + 2} = 33 - - (2)$

On adding equation (1) and equation (2), we get

$\rm :\longmapsto\:\dfrac{20}{2x + 1} + \dfrac{20}{y + 2} = 60$

$\rm :\longmapsto\:\dfrac{1}{2x + 1} + \dfrac{1}{y + 2} = 3 - - - (3)$

On Subtracting equation (2) from equation (1), we get

$\rm :\longmapsto\:\dfrac{ - 6}{2x + 1} + \dfrac{6}{y + 2} = - 6$

$\rm :\longmapsto\: - \: \dfrac{1}{2x + 1} + \dfrac{1}{y + 2} = - 1 - - - (4)$

On adding equation (3) and equation (4), we get

$\rm :\longmapsto\:\dfrac{2}{y + 2} = 2$

$\rm :\longmapsto\:\dfrac{1}{y + 2} = 1$

$\rm :\longmapsto\:y + 2 = 1$

$\bf\implies \:y = - \: 1$

On Subtracting equation (4) from equation (3), we get

$\rm :\longmapsto\:\dfrac{2}{2x + 1} = 4$

$\rm :\longmapsto\:\dfrac{1}{2x + 1} = 2$

$\rm :\longmapsto\:4x + 2 = 1$

$\rm :\longmapsto\:4x = 1 - 2$

$\rm :\longmapsto\:4x = - 1$

$\bf\implies \:x = \: - \: \dfrac{1}{4}$