Show that-the following equation has a unique solution: $3 x, + 5 y = 12, 5 x + 3 y = 4$

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Solution

Given $: -$
$\begin{matrix} 3 x + 5 y = 12 5 x + 3 y = 4 \end{matrix}$
The system of equations has unique solution if $,$
Ratio of coefficients of x is not equal to ratio of coefficients of $y .$
Now $,$
Coefficients of $x = 3, 5$
Coefficients of $y = 5, 3$
Now $,$ $3 / 5 \neq 5 / 3$ $
Hence $,$ $T h e g i v e n s y s t e m o f e q u a t i o n s h a v e u n i q u e s o l u t i o n s$ .$

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