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ICSE Class X Math 2014 Paper

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Question : 6 of 52
Marks: +1, -0
Find x,yx, y if
(−2031)(−12x)+3(−21)\begin{pmatrix} -2 & 0 \\ 3 & 1 \end{pmatrix}\begin{pmatrix} -1 \\ 2x \end{pmatrix}+3\begin{pmatrix} -2 \\ 1 \end{pmatrix} =2(y3)  ". "  =2\begin{pmatrix} y \\ 3 \end{pmatrix} \; \text{". "} \;
Solution:  
Given
(−2031)(−12x)+3(−21)  \begin{pmatrix} -2 & 0 \\ 3 & 1 \end{pmatrix}\begin{pmatrix} -1 \\ 2x \end{pmatrix}+3\begin{pmatrix} -2 \\ 1 \end{pmatrix} \; =2(y3)=2\begin{pmatrix} y \\ 3 \end{pmatrix}
(−2×−1+0×2x3×−1+1×2x)+(−63)  \begin{pmatrix} -2 \times -1 + 0 \times 2x \\ 3 \times -1 + 1 \times 2x \end{pmatrix}+\begin{pmatrix} -6 \\ 3 \end{pmatrix} \; =(2y6)=\begin{pmatrix} 2y \\ 6 \end{pmatrix}
(2−3+2x)+(−63)  \begin{pmatrix} 2 \\ -3+2x \end{pmatrix}+\begin{pmatrix} -6 \\ 3 \end{pmatrix} \; =(2y6)=\begin{pmatrix} 2y \\ 6 \end{pmatrix}
(2−6−3+2x+3)  =(2y6)\begin{pmatrix} 2-6 \\ -3+2x+3 \end{pmatrix} \; =\begin{pmatrix} 2y \\ 6 \end{pmatrix}
(−42x)  =(2y6)\begin{pmatrix} -4 \\ 2x \end{pmatrix} \; =\begin{pmatrix} 2y \\ 6 \end{pmatrix}
Comparing the cofficiant
  2y  =−4   and   2x=6\;2y\;=-4 \;\text{ and }\; 2x=6
⇒y  =−2   and   x=3\Rightarrow y\;=-2 \;\text{ and }\; x=3
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