Solve the following system of equations:
$x+y=5xy$
$3x+2y=13xy$

Given:

The given system of equations is:

$x+y=5xy$

$3x+2y=13xy$

To do:

We have to solve the given system of equations.

Solution:

The given system of equations can be written as,

$x+y=5xy$

$2(x+y)=2(5xy)$   (Multiplying by 2 on both sides)

$2x+2y=10xy$---(i)

$3x+2y=13xy$---(ii)

Subtracting equation (i) from equation (ii), we get,

$3x+2y-2x-2y=13xy-10xy$

$x=3xy$

$\frac{xy}{x}=\frac{1}{3}$

$y=\frac{1}{3}$

Using $y=\frac{1}{3}$ in equation (i), we get,

$2x+2(\frac{1}{3})=10x(\frac{1}{3})$

$2x+\frac{2}{3}=\frac{10}{3}x$

$\frac{10}{3}x-2x=\frac{2}{3}$

$(\frac{10-3\times2}{3})x=\frac{2}{3}$

$(10-6)x=2$

$4x=2$

$x=\frac{2}{4}$

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

Therefore, the solution of the given system of equations is $x=\frac{1}{2}$ and $y=\frac{1}{3}$. 

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Updated on: 10-Oct-2022

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