Which system of equations has no solutions?
Understand the Problem
The question is asking about systems of equations in mathematics that do not have any solutions, typically involving parallel lines in two-dimensional space where the lines do not intersect.
Answer
The system of equations has no solutions.
Answer for screen readers
The system of equations has no solutions.
Steps to Solve
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Identify Parallel Lines Determine if the equations of the lines in question are parallel. This typically occurs when they have the same slope but different y-intercepts.
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Examine the Equation Forms For example, if we have two linear equations: $$ y = mx + b_1 $$ $$ y = mx + b_2 $$ where $m$ is the slope and $b_1 \neq b_2$ indicates different y-intercepts.
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Set Up the Slopes For parallel lines, you can see that both equations have the same slope $m$. Hence, if you can confirm the slopes of both equations are equal, then they are parallel.
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Conclusion of No Solution Since parallel lines never intersect, conclude that the system of equations has no solutions.
The system of equations has no solutions.
More Information
This situation is common in mathematics when analyzing systems of linear equations. It highlights the concept of parallel lines in geometry, which never meet.
Tips
- Confusing equal slopes with parallel lines. Remember, the y-intercepts must differ for the lines to be parallel.
- Failing to simplify equations properly before comparing. Always make sure the lines are in the same format for accurate analysis.
