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In a system of linear equations, what does it mean if the equations are dependen
In a system of linear equations, what does it mean if the equations are dependent?
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Practice Questions
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Q1
In a system of linear equations, what does it mean if the equations are dependent?
They have exactly one solution.
They have infinitely many solutions.
They have no solutions.
They are inconsistent.
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Dependent equations represent the same line, leading to infinitely many solutions.
Questions & Step-by-step Solutions
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Q
Q: In a system of linear equations, what does it mean if the equations are dependent?
Solution:
Dependent equations represent the same line, leading to infinitely many solutions.
Steps: 5
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Step 1: Understand that a system of linear equations consists of two or more equations.
Step 2: Recognize that each equation represents a line on a graph.
Step 3: Identify what it means for equations to be dependent: it means they describe the same line.
Step 4: Realize that if two equations are dependent, they do not intersect at a single point; instead, they overlap completely.
Step 5: Conclude that because the lines are the same, there are infinitely many solutions (any point on the line is a solution).
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