A system of n linear equations in n unknowns has no solution, one solution, or infinitely many solutions. This is ALWAYS true.
It is easy to visualize in the two dimensional case. As you know, a linear equation in two unknowns can be graphed as a straight line on a Cartesian plane. If you have two such equations, their simultaneous solution is where their two lines intersect. Right? This is basic stuff. However, if the lines are parallel, the two lines never intersect, which means that their is no simultaneous solution. If the two equations are represented by the SAME line, the "two" lines intersect everywhere, which means that every point on the line is a simultaneous solution.
If you follow that, then how to solve the problem becomes this: for what values of t are the lines representing the equations parallel and so intersect nowhere, for what values of t are the two lines identical and so "intersect" everywhere, and for what values of t are the two lines distinct but not parallel and so intersect at a single point.
Show us far you can get with that set of starting hints.