In Algebra 1, a system of equations is a set of two or more equations containing the same variables. Solving a system of equations means finding values for the variables that satisfy all equations simultaneously. Graphing, substitution, and elimination are common methods used to find these solutions. Worksheets provide practice in applying these methods and understanding the different types of solutions (one solution, no solution, or infinitely many solutions).
Match the terms with their definitions:
| Term | Definition |
|---|---|
| 1. System of Equations | A. A method to solve systems by eliminating one variable. |
| 2. Solution | B. A set of two or more equations with the same variables. |
| 3. Substitution | C. The point(s) where the lines intersect. |
| 4. Elimination | D. A method to solve systems by solving for one variable and plugging it into another equation. |
| 5. Ordered Pair | E. A set of values for the variables that satisfies all equations. |
Match the following (Answers below):
A ________ of equations is a set of two or more equations. Solving a system means finding values for the ________ that make all equations true. The ________ method involves solving one equation for one variable and substituting that expression into the other equation. The ________ method involves adding or subtracting the equations to eliminate one variable. If the lines are parallel, there is ________ solution.
Word Bank: no, system, elimination, variables, substitution
Explain, in your own words, why a system of equations might have no solution. Give an example of such a system.
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