That they, along with the equations, are invisible!
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The system of equations can have zero solutions, one solution, two solutions, any finite number of solutions, or an infinite number of solutions. If it is a system of LINEAR equations, then the only possibilities are zero solutions, one solution, and an infinite number of solutions. With linear equations, think of each equation describing a straight line. The solution to the system of equations will be where these lines intersect (a point). If they do not intersect at all (or maybe two of the lines intersect, and the third one doesn't) then there is no solution. If the equations describe the same line, then there will be infinite solutions (every point on the line satisfies both equations). If the system of equations came from a real world problem (like solving for currents or voltages in different parts of a circuit) then there should be a solution, if the equations were chosen properly.
Two or more straight lines meeting at one point.
None, one or an infinite number. In graph form, the three correspond to: None = Parallel lines One = Interscting lines Infinite = Coincident lines.
There must be fewer independent equation than there are variables. An equation in not independent if it is a linear combination of the others.
They are all lines. Their equations are written in the slope-intercept form, where we clearly can see if they just intersect, or are perpendicular to each other, or parallel, or coincide.