Question

Solve 1/x + 1/y =7, 2/x + 3/y =17​

Answer 1

$\huge\rm\color{blue}{Answer :}$

$x = \frac{1}{4} , y = \frac{1}{3}$

$\small\textbf\color{teal}{Step-by-step explanation :}$

Given a pair of linear equations. We need to find the value of x and y from this equations by elimination method.

In elimination method we can use addition or subtraction.

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$\begin{gathered}\frac{2}{x}+\frac{3}{y}=17\\\\= > 2y+3x=17xy...(1)\\\\\frac{1}{x} +\frac{1}{y}=7\\\\ = > y+x=7xy\end{gathered}$

$\small\textbf\color{teal}{Now multiply with 2 on both sides, we get}$

$\begin{gathered}2y+3x-(2y+2x)=17xy-14xy\\\\= > 3x-2x=3xy\\\\= > x=3xy\\\\= > y=\frac{1}{3}\end{gathered}$

$\small\textbf\color{teal}{sub. y = 1/3 in (2) , we get}$

$\: \:\begin{gathered} 2(\frac{1}{3} )+2x=14x(\frac{1}{3} )\\\\\frac{2}{3}+2x=\frac{14x}{3}\\\\ \frac{6}{3}+6x=14x\\\\ 2+6x=14x\\\\ 2=8x\\\\x=\frac{1}{4}\end{gathered}$

$\: \: \: \: \: \: \: \: \:$Thankyou :)