Question: In a system of linear equations, what does it mean if the equations are dependent?
Options:
They have exactly one solution.
They have infinitely many solutions.
They have no solutions.
They are inconsistent.
Correct Answer: They have infinitely many solutions.
Solution:
Dependent equations represent the same line, leading to infinitely many solutions.
In a system of linear equations, what does it mean if the equations are dependen
Practice Questions
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.
Questions & Step-by-Step Solutions
In a system of linear equations, what does it mean if the equations are dependent?
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).
Dependent Equations – Dependent equations are those that do not provide new information and represent the same geometric line in a system of linear equations.
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