๐ Topic Summary
Solving a system of equations by graphing involves plotting each equation on the same coordinate plane. The solution to the system is the point where the lines intersect. If the lines are parallel, there is no solution. If the lines are the same, there are infinitely many solutions. This method provides a visual representation of the solution, making it easier to understand the relationship between the equations.
To solve, graph each equation carefully. Look for the point where the lines cross. The coordinates of that point (x, y) are the solution to the system. Always check your solution by plugging the x and y values back into the original equations to make sure they work!
๐ง Part A: Vocabulary
Match the term with its definition:
| Term |
Definition |
| 1. System of Equations |
A. A point (x, y) that satisfies all equations in the system. |
| 2. Coordinate Plane |
B. Two or more equations considered together. |
| 3. Solution to a System |
C. The x-value where a line crosses the x-axis. |
| 4. X-intercept |
D. A plane formed by a horizontal number line (x-axis) and a vertical number line (y-axis). |
| 5. Y-intercept |
E. The y-value where a line crosses the y-axis. |
Match the correct term to the definition:
- 1 - B
- 2 - D
- 3 - A
- 4 - C
- 5 - E
๐ Part B: Fill in the Blanks
Complete the following sentences using the words provided: intersection, solution, graph, parallel, infinite.
- When solving a system of equations by graphing, you _________ each equation on the same coordinate plane.
- The _________ to the system is the point where the lines cross.
- If the lines are _________, there is no _________.
- If the lines are the same, there are _________ solutions.
Answer Key:
- Graph
- Solution
- Parallel; solution
- Infinite
๐ค Part C: Critical Thinking
Explain, in your own words, why solving a system of equations by graphing provides a visual understanding of the solution compared to solving algebraically.