This is called a Cartesian coordinate system, which is named for the French mathematician and philosopher René Descartes (1596-1650).
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The origin is where the two intersect. This is where both number lines are 0.
one solution; the lines that represent the equations intersect an infinite number of solution; the lines coincide, or no solution; the lines are parallel
a coordinate plane
Perpendicular lines form right angles when they intersect.
Graphically, it is the point of intersection where the lines (in a linear system) intersect. If you have 2 equations and two unknowns, then you have a 2 lines in a plane. The (x,y) coordinates of the point where the 2 lines intersect represent the values which satisfies both equations. If there are 3 equations and 3 unknowns, then you have lines in 3 dimensional space. If all 3 lines intersect at a point then there is a solution to the system. With more than 3 variables, it is difficult to visualize more dimensions, though.