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Matrices — Mathematics STD 10 — Question

ICSE BoardEnglish MediumSTD 10MathematicsMatrices2 Marks
Question
If $[x, y]\left[\begin{array}{l}x \\ y\end{array}\right]=[25]$ and $\left[\begin{array}{ll}-x & y\end{array}\right]\left[\begin{array}{c}2 x \\ y\end{array}\right]=[-2]$ find $x$ and $y$ if $x, y \in Z ($integer$)$  
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Answer

$[x, y]\left[\begin{array}{l}x \\ y\end{array}\right]=[25]$
$x^2+y^2=25$
and
$-2 x^2+y^2=-2$
$x, y \in Z ($interger$)$
If can observed that that above two equation are satisfied when $x= \pm 3$ and $\mathrm{y}=\pm 4$

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