with 5 digits

> Digits:=5;

> ill:=array(1.. 3,1.. 4,[[6,6,3.00001,30.00002],[10,8,4.00003,42.00006],[6,4,2.00002,22.00004]]);

> glinsys(ill);

Multiply row 1 by 1/6

> ill1:=linalg[mulrow](ill,1,1/ill[1,1]);

Add to row 2 -10 times row 1

> ill2:=linalg[addrow](ill1,1,2,-ill1[2,1]);

> glinsys(ill2);

Add to row 3 -6 times row 1

> ill3:=linalg[addrow](ill2,1,3,-ill2[3,1]);

> glinsys(ill3);

Multiply row 2 by -1/2

> ill4:=linalg[mulrow](ill3,2,1/ill3[2,2]);

Add to row 1 -1 times row 2

> ill5:=linalg[addrow](ill4,2,1,-ill4[1,2]);

> glinsys(ill5);

Add to row 3 2 times row 2

> ill6:=linalg[addrow](ill5,2,3,-ill5[3,2]);

> glinsys(ill6);

When Digits is 5, the method just used shows that there are an infinite number of solutions.

>