Question

if [2 6 4 2][3x 2]+2[3 4]=5[4 y]
find values of x and y.​

Answer 1

Given :   $\left[\begin{array}{ccc}2&6 \\4&2\end{array}\right] \left[\begin{array}{ccc}3x\\ 2\end{array}\right] + 2 \left[\begin{array}{ccc}3\\ 4\end{array}\right] = 5\left[\begin{array}{ccc}4\\ y\end{array}\right]$

To Find :  Values of x &  y

Solution:

$\left[\begin{array}{ccc}2&6 \\4&2\end{array}\right] \left[\begin{array}{ccc}3x\\ 2\end{array}\right] + 2 \left[\begin{array}{ccc}3\\ 4\end{array}\right] = 5\left[\begin{array}{ccc}4\\ y\end{array}\right]$

$\left[\begin{array}{ccc}2&6 \\4&2\end{array}\right] \left[\begin{array}{ccc}3x\\ 2\end{array}\right] =\left[\begin{array}{ccc}6x+12 \\12x+4\end{array}\right]$

$\left[\begin{array}{ccc}6x+12\\ 12x+4\end{array}\right] + 2 \left[\begin{array}{ccc}3\\ 4\end{array}\right] = 5\left[\begin{array}{ccc}4\\ y\end{array}\right]$

$\left[\begin{array}{ccc}6x+12\\ 12x+4\end{array}\right] + \left[\begin{array}{ccc}6\\ 8\end{array}\right] = \left[\begin{array}{ccc}20\\ 5y\end{array}\right]$

$\left[\begin{array}{ccc}6x+18\\ 12x+12\end{array}\right]= \left[\begin{array}{ccc}20\\ 5y\end{array}\right]$

6x + 18 = 20  => 6x = 2  => x  = 1/3

12x  + 12 = 5y

=> 12(1/3) + 12 = 5y

=> 4 + 12 = 5y

=>16 = 5y

=> y = 16/5

x = 1/3  and  y = 16/5

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