Question 874961
1w+1x+1y+1z=2
1w+2x+3y+4z=2
2w+3x+5y+9z=2
1w+1x+2y+7z=2

first get the determinant of 
{1,1,1,1
{1,2,3,4}
{2,3,5,9}
{1,1,2,7}
which is D=2
then get the determinant of 
Dw =-6 from below
 2,1,1,1
 2,2,3,4
 2,3,5,9
 2,1,2,7

Dx=16
1,2,1,1
1,2,3,4
2,2,5,9
1,2,2,7

Dy=-10
1,1,2,1
1,2,2,4
2,3,2,9
1,1,2,7

Dz=2
1,1,1,2
1,2,3,2
2,3,5,2
1,1,2,2

w=Dw/D=-6/2=-3
x=Dx/D=16/2=8
y=Dy/D=-10/2=-5
z=Dz/D=2/2=1

and there you have it.