Question 949341
 A system of equations is consistent if it has at least one solution. There are two types:
TYPE 1:Independent system has exactly one solution. The graph of this system is intersecting lines.
Example:
y=2x+3
y=(-1/2)x+3
This system has exactly one solution, the intersection at point (0,3)
GRAPH OF CONSISTENT INDEPENDENT SYSTEM:
{{{ graph( 800, 800, -5, 5, -5, 5, 2x+3, -0.5x+3) }}} 
TYPE 2:Consistent Dependent systems have infinite solutions Their graphs are the same line.  Examples of these are multiples of an equation. 
Example:
y=2X-3
y=(4X-6)/2
GRAPH OF CONSISTENT DEPENDENT EQUATIONS:
{{{ graph( 800, 800, -5, 5, -5, 5, 2x-3, (4x-6)/2)}}}
This graph looks like one line because the lines overlap, so there are infinite solutions.   

INCONSISTENT SYSTEMS HAVE NO SOLUTIONS (No common solution)
Examples of this are parallel lines.
y=2x+2
y=2x+6
GRAPH OF INCONSISTENT SYSTEM:
{{{ graph( 800, 800, -5, 5, -5, 5, 2x+2, 2x+6)}}}