📚 Topic Summary
The elimination method is a technique used to solve systems of linear equations. The core idea is to manipulate the equations (by multiplying them by constants) so that when you add or subtract the equations, one of the variables is eliminated. This leaves you with a single equation in one variable, which you can easily solve. After finding the value of one variable, you can substitute it back into one of the original equations to find the value of the other variable.
This method is particularly useful when the coefficients of one of the variables are the same or easily made the same. By strategically eliminating variables, you can simplify complex systems into manageable single-variable equations.
🧮 Part A: Vocabulary
Match the following terms with their definitions:
| Term |
Definition |
| 1. System of Linear Equations |
A. A method to solve systems by adding or subtracting equations. |
| 2. Elimination Method |
B. A solution that satisfies all equations in the system. |
| 3. Solution of a System |
C. Equations with the same solution set. |
| 4. Equivalent Systems |
D. Two or more linear equations considered together. |
| 5. Coefficient |
E. The numerical factor of a term. |
Match the correct term to its definition.
✍️ Part B: Fill in the Blanks
The elimination method involves manipulating equations to ______ one of the variables. This is achieved by multiplying one or both equations by a suitable ______. After eliminating a variable, you solve for the remaining variable and ______ this value back into one of the original equations to find the value of the ______ variable. This method is especially useful when the ______ of one of the variables are the same or easily made the same.
🤔 Part C: Critical Thinking
Explain, in your own words, why it is sometimes necessary to multiply one or both equations by a constant before applying the elimination method. Provide an example to illustrate your explanation.