Here are the terms matched with their correct explanations regarding possible solutions to a system of equations:
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Two lines have the same slope and y-intercept: This corresponds to the situation where the lines are identical or represent the same line. Thus, there are infinitely many solutions since every point on the line is a solution.
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Two lines intersect at one point: This indicates that there is a unique solution to the system of equations, meaning the lines are not parallel and cross at a single point.
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Two lines are parallel: This means that the lines have the same slope but different y-intercepts, resulting in no solution since they never meet.
So, in summary:
- Two lines have the same slope and y-intercept: Infinitely many solutions (identical lines)
- Two lines intersect at one point: One unique solution
- Two lines are parallel: No solution