Answer: The required value of x is 1.
Step-by-step explanation: We are to use the Cramer's rule to find the value of x in the following system of equations :
[tex]x+3y=16~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\3x+y=8~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)[/tex]
By Cramer's rule, we get
[tex]\dfrac{x}{D_1}=\dfrac{y}{D_2}=\dfrac{1}{D},[/tex]
where
[tex]D_1=\begin{bmatrix}16 & 3\\ 8 & 1\end{bmatrix}=16\times1-8\times3=16-24=-8,\\\\\\\\D_2=\begin{bmatrix}1 & 16\\ 3 & 8\end{bmatrix}=8\times1-16\times3=8-48=-40,\\\\\\\\D=\begin{bmatrix}1 & 3\\ 3 & 1\end{bmatrix}=1\times1-3\times3=1-9=-8.[/tex]
Therefore, we get
[tex]\dfrac{x}{-8}=\dfrac{y}{-40}=\dfrac{1}{-8}\\\\\\\Rightarrow x=\dfrac{-8}{-8},~~~y=\dfrac{-40}{-8}\\\\\\\Rightarrow x=1,~~y=5.[/tex]
Thus, the required value of x is 1.
