Question

Using Cramer’s Rule, what is the value of x in the system of linear equations below?

x+3y=16
3x+y=8

Answer 1

we know that
Cramer's rule works as follows:
x+3y=16
3x+y=8
Then
x=Dx/D
y=Dy/D
where Dx,Dy,D are 2x2 matrices formed from of coefficients and right hand side.
D=
1 3
3 1
=1-9=-8
Dx=matrix D with first column replaced by the vector [16,8]=
16 3
8 1
=16-24=-8
Dy=matrix D with second column replaced by the vector [16,8]=
1 16
3 8
=8-48=-40

therefore
x=-8/-8=1
y=--40/-8=5

the answer is
x=1
y=5

Answer 2

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 :

`x+3y=16~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\3x+y=8~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)`

By Cramer's rule, we get

`(x)/(D_1)=(y)/(D_2)=(1)/(D),`

where

`D_1=\begin{bmatrix}16 & 3\\ 8 & 1\end{bmatrix}=16*1-8*3=16-24=-8,\\\\\\\\D_2=\begin{bmatrix}1 & 16\\ 3 & 8\end{bmatrix}=8*1-16*3=8-48=-40,\\\\\\\\D=\begin{bmatrix}1 & 3\\ 3 & 1\end{bmatrix}=1*1-3*3=1-9=-8.`

Therefore, we get

`(x)/(-8)=(y)/(-40)=(1)/(-8)\\\\\\\Rightarrow x=(-8)/(-8),~~~y=(-40)/(-8)\\\\\\\Rightarrow x=1,~~y=5.`

Thus, the required value of x is 1.