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

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

Check:
x+3y=1+3(5)=16
3x+y=3(1)+5=8   ok.