Find x and y if {pmatrix} x & 3x \\ y & 4y ...

ICSE Class X Math 2013 Paper

Question : 32 of 46

Marks: +1, -0

Find

x

and

y

\begin{pmatrix} x & 3x \\ y & 4y \end{pmatrix}\begin{pmatrix} 2 \\ 1 \end{pmatrix}=\begin{pmatrix} 5 \\ 12 \end{pmatrix}

Solution:

Given :

\begin{pmatrix} x & 3x \\ y & 4y \end{pmatrix}\begin{pmatrix} 2 \\ 1 \end{pmatrix}\;=\begin{pmatrix} 5 \\ 12 \end{pmatrix}

\begin{pmatrix} 2x+3x \\ 2y+4y \end{pmatrix}\;=\begin{pmatrix} 5 \\ 12 \end{pmatrix}

\begin{pmatrix} 5x \\ 6y \end{pmatrix}\;=\begin{pmatrix} 5 \\ 12 \end{pmatrix}

\therefore 5x=5

\Rightarrow x=1

and

6y=12

\Rightarrow y=2

Hence,

x=1

and

y=2

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