📚 Topic Summary
The elimination method is a technique used to solve systems of equations by adding or subtracting the equations to eliminate one variable. When the coefficients of the variables you want to eliminate aren't opposites or the same, you'll need to multiply one or both equations by a constant to make them so. This prepares the system for straightforward elimination, leading you to the solution much faster! Let's put this into practice.
🧮 Part A: Vocabulary
Match each term with its correct definition:
| Term |
Definition |
| 1. System of Equations |
A. A method to solve systems by adding or subtracting equations. |
| 2. Elimination Method |
B. The point where two lines intersect on a graph. |
| 3. Solution |
C. Two or more equations containing the same variables. |
| 4. Coefficient |
D. Multiplying an equation by a constant to change the coefficients. |
| 5. Multiplication Property of Equality |
E. The number multiplied by a variable in an algebraic term. |
(Match the terms with the definitions. For example: 1-C, 2-A, etc.)
✏️ Part B: Fill in the Blanks
Complete the following paragraph using the words provided (eliminate, variable, multiplication, system, solution):
To solve a ______ of equations using the elimination method with ______, the goal is to ______ one ______ by making the coefficients opposites. After eliminating the variable, solve for the remaining variable. Substitute that value back into one of the original equations to find the ______ to the system.
🤔 Part C: Critical Thinking
Explain, in your own words, why it is sometimes necessary to multiply one or both equations in a system before using the elimination method. Provide an example.