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Determinants — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsDeterminants2 Marks
Question
If $\left|\begin{array}{ll}2 & 3 \\ y & x\end{array}\right|=3,\left|\begin{array}{ll}x & y \\ 4 & 2\end{array}\right|=5$ then find value of $x$ and $y$.
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Answer

Given : $\left|\begin{array}{ll}2 & 3 \\ y & x\end{array}\right|=3,\left|\begin{array}{ll}x & y \\ 4 & 2\end{array}\right|=5$
$\therefore 2 x-3 y=3 .....(1)$
$2 x-4 y=5 .......(2) $
Subtract equation $(2)$ from equation $(1)$
$y=-2$
On putting the value of $y$ in equation $(1)$
$2 x-3 \times(-2) =3$
$\Rightarrow 2 x+6 =3$
$\Rightarrow x =\frac{-3}{2}$

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