21.1.4 - Consistency of a System
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Practice Questions
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Define a consistent system of linear equations.
💡 Hint: Think about what it means for equations to intersect.
What is an inconsistent system?
💡 Hint: Consider what happens when two lines are parallel.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What type of system has at least one solution?
💡 Hint: Think about what happens when lines intersect.
True or False: An inconsistent system has no solutions.
💡 Hint: Remember the definition of inconsistency.
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Challenge Problems
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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.
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.
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