> 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!