Solving a system of equations by graphing involves finding the point(s) where the lines representing the equations intersect. The coordinates of the intersection point(s) represent the solution(s) to the system. If the lines are parallel, there is no solution. If the lines are the same, there are infinitely many solutions.
Match the following terms with their definitions:
| Term | Definition |
|---|---|
| 1. System of Equations | A. Lines with the same slope and y-intercept. |
| 2. Solution to a System | B. Two or more equations with the same variables. |
| 3. Intersection Point | C. A system with no solution. |
| 4. Infinite Solutions | D. The point(s) where two or more lines cross. |
| 5. No Solution | E. Values for the variables that make all equations true. |
Correct Matches: 1-B, 2-E, 3-D, 4-A, 5-C
Solving systems of equations by ____________ involves graphing each equation on the same coordinate plane. The ____________ to the system is/are the ____________ of the point(s) where the lines intersect. If the lines are ____________, there is no solution.
Answer: solving, solution, coordinates, parallel
Explain in your own words why a system of equations might have no solution when solved by graphing. What does this look like on a graph?
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