Question

2x+3/y=5, 5x+2/y=3 by elimination method​

Answer 1

Step-by-step explanation:

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Answer 2

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

Given pair of equations are

$\rm :\longmapsto\:2x + \dfrac{3}{y} = 5 - - - (1)$

and

$\rm :\longmapsto\:5x + \dfrac{2}{y} = 3 - - - (2)$

On multiply equation (1) by 2 and equation (2) by 3, we get

$\rm :\longmapsto\:4x + \dfrac{6}{y} = 10 - - - (3)$

and

$\rm :\longmapsto\:15x + \dfrac{6}{y} = 9 - - - (4)$

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

$\rm :\longmapsto\: - 11x = 1$

$\rm \implies\:\boxed{ \tt{ \: x \: = \: - \: \frac{1}{11} \: }}$

On substituting the value of x in equation (1), we get

$\rm :\longmapsto\:\dfrac{ - 2}{11} + \dfrac{3}{y} = 5$

$\rm :\longmapsto\: \dfrac{3}{y} = 5 + \dfrac{2}{11}$

$\rm :\longmapsto\: \dfrac{3}{y} = \dfrac{55 + 2}{11}$

$\rm :\longmapsto\: \dfrac{3}{y} = \dfrac{57}{11}$

$\rm :\longmapsto\: \dfrac{1}{y} = \dfrac{19}{11}$

$\rm \implies\:\boxed{ \tt{ \: y \: = \: \frac{11}{19} \: }}$

Therefore,

$\red{\begin{gathered}\begin{gathered}\bf\: \rm :\longmapsto\:-\begin{cases} &\bf{x = - \: \dfrac{1}{11} } \\ \\ &\bf{y = \: \dfrac{11}{19} } \end{cases}\end{gathered}\end{gathered}}$

Verification

Consider the equation

$\rm :\longmapsto\:2x + \dfrac{3}{y} = 5$

On substituting the values of x and y, we get

$\rm :\longmapsto\:\dfrac{ - 2}{11} + \dfrac{3 \times 19}{11} = 5$

$\rm :\longmapsto\:\dfrac{ - 2}{11} + \dfrac{57}{11} = 5$

$\rm :\longmapsto\: \dfrac{ - 2 + 57}{11} = 5$

$\rm :\longmapsto\: \dfrac{55}{11} = 5$

$\bf\implies \:5 = 5$

Hence, Verified