have infinitely many solutions, because every point on the first line is also on the second line.
In the 3x3 case, an equation of the form represents a plane in three-dimensional space. It will always contain the whole of the line Again, you can verify that by plugging and into the equation and checking that it is satisfied. In particular, if you put t=2 then you see that the point lies in the plane.
So if you take any number of planes of that form, their intersection will always contain that line. For two or more planes, the intersection will normally be exactly equal to that line. But as in the 2x2 case, there is an exceptional case that arises if all the equations are multiples of each other and therefore represent the same plane. In that case, every point of the plane will give a solution to the equations.