Question

Solve by matrix method


`(6)/(x) - (2)/(y) = 1`

`3x - 2y = 2xy`
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Answer 1

x=2 , y=1

Explanation:

`(6)/(x)-(2)/(y)=1\quad ,\quad 3x-2y=2xy\\(6)/(x)-(2)/(y)=1\quad ,\quad -(2)/(x)+(3)/(y)=2\\\Delta=\left[\begin{array}{cc}6&-2\\-2&3\end{array}\right] =14\\\Delta_(1/x)=\left[\begin{array}{cc}1&-2\\2&3\end{array}\right] =7\\\Delta_(1/y)=\left[\begin{array}{cc}6&1\\-2&2\end{array}\right] =14\\1/x=\Delta_(1/x)/\Delta=1/2\quad,\quad 1/y=\Delta_(1/y)/\Delta=1\Rightarrow x=2,y=1`