📚 Topic Summary
Graphing linear systems involves finding the solution (or solutions) that satisfy two or more linear equations. Each equation represents a line on a coordinate plane, and the solution is the point where the lines intersect. If the lines are parallel, there's no solution; if they're the same line, there are infinitely many solutions.
This practice exam will help you solidify your understanding of graphing linear systems by testing your knowledge of key vocabulary, your ability to fill in the blanks related to core concepts, and your critical thinking skills through an open-ended question. Good luck!
🔤 Part A: Vocabulary
Match each term with its correct definition:
| Terms |
Definitions |
| 1. Linear Equation |
A. A point where two or more lines intersect. |
| 2. System of Equations |
B. Equations that have the same slope and y-intercept. |
| 3. Solution |
C. An equation whose graph is a straight line. |
| 4. Parallel Lines |
D. Two or more equations considered together. |
| 5. Coincident Lines |
E. Lines that never intersect and have the same slope. |
Match the term to the correct definition (e.g., 1-C, 2-D, etc.).
✍️ Part B: Fill in the Blanks
Complete the following paragraph using the words provided below:
When graphing a system of linear equations, the ________ represents the point where the lines _______. If the lines are _______, they have no solution. If the lines are _______, they have infinite solutions.
Word Bank: intersect, solution, parallel, coincident
🤔 Part C: Critical Thinking
Explain, in your own words, how you can determine the number of solutions a system of linear equations has without graphing the equations.