21.1.4. Consistency of a System

Try these first

1. 1.

   Define a consistent system of linear equations.

   Hint

   Think about what it means for equations to intersect.

2. 2.

   What is an inconsistent system?

   Hint

   Consider what happens when two lines are parallel.

3. 3.

   What type of system has at least one solution?

   • Inconsistent
   • Consistent
   • Infinite

   Hint

   Think about what happens when lines intersect.

4. 4.

   True or False: An inconsistent system has no solutions.

   • True
   • False

   Hint

   Remember the definition of inconsistency.

5. 5.

   Given the equations x + y = 4 and 2x + 2y = 8, determine the consistency of this system and explain why.

   Hint

   Graph the equations or manipulate them algebraically.

6. 6.

   If a system has three variables (x, y, z), but only one equation, explain the implications for consistency.

   Hint

   Consider how the lack of constraints affects solutions.