解：

x1-2x2+3x3-4x4=4,

0+x2-x3+x4=-3,

x1+3x3+0+x4=1,

0-7x2+3x3+x4=-3

D=

1 -2 3 -4

0 1 -1 1

1 3 0 1

0 -7 3 1

=16

D1=

4 -2 3 -4

-3 1 -1 1

1 3 0 1

-3 -7 3 1

=-128

D2=

1 4 3 -4

0 -3 -1 1

1 1 0 1

0 -3 3 1

=48

D3=

1 -2 4 -4

0 1 -3 1

1 3 1 1

0 -7 -3 1

=96

D4=

1 -2 3 4

0 1 -1 -3

1 3 0 1

0 -7 3 -3

=0

所以x1=D1/D=-8

x2=D2/D=3

x3=D3/D=6

x4=D4/D=0