When graphing systems of equations, parallel lines indicate there is no solution. This is because parallel lines, by definition, never intersect. In the context of systems of equations, the solution represents the point where two or more lines meet. If the lines never meet, there's no solution that satisfies both equations simultaneously. These lines will have the same slope but different y-intercepts.
To identify parallel lines resulting in no solution, look for equations that, when graphed, produce lines that run alongside each other without ever crossing. Remember, same slope, different y-intercept!
| Term | Definition |
|---|---|
| 1. Parallel Lines | A. The point where two lines intersect. |
| 2. Slope | B. Lines in the same plane that never intersect. |
| 3. Y-intercept | C. A system of equations with no solution. |
| 4. No Solution | D. The value of y where the line crosses the y-axis. |
| 5. Intersection | E. A number that describes both the direction and the steepness of the line. |
Match the term with its correct definition.
Parallel lines have the same ________ but different ________. When graphed, these lines never ________, indicating that the system of equations has ________ solution. This happens because there is no point that satisfies ________ equations simultaneously.
Explain, in your own words, why a system of equations represented by parallel lines has no solution. Use examples to illustrate your explanation.
Please log in to post your answer.
Log InEarn 2 Points for answering. If your answer is selected as the best, you'll get +20 Points! 🚀