A system of equations is said to be consistent if it has solutions.
• When a consistent system has ,exactly one solution,, it is ,independent,. These systems form an X-shape when graphed.
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• When a consistent system has ,infinite solutions, ,it is ,dependent. ,When you graph the equations, both equations represent the same line.
An inconsistent system has no solutions. They form parallel lines.
In the given exercise:
System A
Parallel lines:
• The system of equations is ,inconsistent,.
,
• This means the system has, No Solution.
System B
X-Shape:
• The system of equations is ,consistent independent.
,
• This means the system has a ,unique solution:
,
• Solution:, (1, -1) ,[from the graph].
System C
A Single Line:
• The system of equations is ,consistent dependent.
,
• This means the system has, infinitely many solutions.