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DETERMINANTS — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsDETERMINANTS5 Marks
Question
Solve the following for x and y.$\begin{bmatrix}3&-4\\9&2\end{bmatrix}\begin{bmatrix}\text{x}\\\text{y}\end{bmatrix}=\begin{bmatrix}10\\2\end{bmatrix}$
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Answer

Here,
$\begin{bmatrix}3&-4\\9&2\end{bmatrix}\begin{bmatrix}\text{x}\\\text{y}\end{bmatrix}=\begin{bmatrix}10\\2\end{bmatrix}$
$\Rightarrow\begin{bmatrix}3\text{x}-4\text{y}\\9\text{x}-2\text{y}\end{bmatrix}=\begin{bmatrix}10\\2\end{bmatrix}$
$\Rightarrow3 \text{x}-4\text{y}=10\ \dots(1)$
$9\text{x}+2 \text{y}=2\ \dots(2)$
Solving both the equation, we get
$\text{x}=\frac{14}{21}$
$=\frac{2}{3}$
Substituting the value of x in eq. (1), we get
$3\times\frac{2}{3}-4\text{y}=10$
$\Rightarrow2-4\text{y}=10$
$\Rightarrow4 \text{y}=-8$
$\Rightarrow\text{y}=-2$
$\therefore\ \text{x}=\frac{2}{3}\text{ and }\text{y}=-2$

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