> with(linalg):with(plots):

`Warning, new definition for norm`

`Warning, new definition for trace`

>

Numerical solutions of linear equations

> solve({x+3*y=4,2*x-y=1},{x,y});

> solve({x+y=2,x+y=4},{x,y});

Notice that when Maple can't find a solution, it returns a blank answer.

> solve({x+3*y=4,-2*x-6*y=-8},{x,y});

Graphical solutions of linear equations

> implicitplot({x+3*y-4,2*x-y-1},x=-1..2,y=-1..2);

> implicitplot({x+y=2,x+y=4},x=-1..2,y=-1..2);

Where did the 2nd line go? We know that there are no solutions to this linear system, so the 2nd line cannot be on top of the first line, since this would give us infinitely many solutions.

>

Answer to where the 2nd line went

> implicitplot({x+y=4},x=-1..2,y=-1..2);

Notice that if I eliminate the 1st equation, then we can't see the line. Looking more closely, we see that the problem is that we have limited the values too much:

> implicitplot({x+y=2,x+y=4},x=-1..2,y=-1..5);

>

> implicitplot({x+3*y=4,-2*x-6*y=-8},x=-1..2,y=-1..2);

Check to see that both lines are shown here.