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

x+3y=16

3x+y=8

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