Question
In $\left[\begin{array}{cc}x+y & 2 \\ 5+z & x y\end{array}\right]=\left[\begin{array}{ll}6 & 2 \\ 5 & 8\end{array}\right]$ find the value of $x, y, z ?$
✓
Answer
On comparing $x+y=6$
$5+z=5$
$x y=8 $
from equation $(1)$ and $(3)$
$x(6-x) =8$
$\Rightarrow 6 x-x^2 =8$
$\Rightarrow x^2-6 x+8 =0$
$\Rightarrow x^2-4 x-2 x+8 =0 $
$ \Rightarrow x(x-4)-2(x-4) =0$
$\Rightarrow (x-4)(x-2) =0$
$\Rightarrow x =4,2 $
$\text { when } x=4, y=6-x=6-4=2$
$\text { when } x=2, y=6-2=4$
from equation $(2), z=0$
$5+z=5$
$x y=8 $
from equation $(1)$ and $(3)$
$x(6-x) =8$
$\Rightarrow 6 x-x^2 =8$
$\Rightarrow x^2-6 x+8 =0$
$\Rightarrow x^2-4 x-2 x+8 =0 $
$ \Rightarrow x(x-4)-2(x-4) =0$
$\Rightarrow (x-4)(x-2) =0$
$\Rightarrow x =4,2 $
$\text { when } x=4, y=6-x=6-4=2$
$\text { when } x=2, y=6-2=4$
from equation $(2), z=0$
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