Question

select the correct answer.

if the graphs of the linear equations in a system are the same line, what does that mean about the possible solution or solutions of the system?

there is exactly one solution.
there is no solution.
there are infinitely many solutions.
the lines in a system cannot graph as the same line.

Explanation:

Analyze the geometric relationship of the system

Using the Systems of Linear Equations knowledge point

$$ \text{The graphs of the linear equations in the system represent the same line.} $$

Determine the number of intersection points

Using the Systems of Linear Equations knowledge point

$$ \text{Every point on the line is a solution, yielding infinitely many solutions.} $$

Answer:

• There is exactly one solution.
• There is no solution.
• There are infinitely many solutions. (Correct answer)
• The lines in a system cannot graph as the same line.