Another service from Omega

Example of a System with No Solutions

Consider the following system of three linear equations in x,y and z: 

>   E1 :=        x - 2*y + z = 3:
>   E2 :=       -x + 4*y     = -1:
>   E3 :=      2*x +     4*z = 12:
>   
> solve({E1,E2,E3},{x,y,z});

This produces no output. In fact, we can see that these equations are incompatible. 

> B1 := E1 + E2;

                               B1 := 2 y + z = 2

> B2 := E3 - 2*E1;

                              B2 := 2 z + 4 y = 6

> 2*B1 - B2;

                                     0 = -2

Which is a contradiction!