📚 Topic Summary
The elimination method is a technique used to solve systems of linear equations. The main idea is to manipulate the equations so that when you add or subtract them, one of the variables cancels out, leaving you with a single equation in one variable. You can then solve for that variable and substitute the value back into one of the original equations to find the value of the other variable.
Before using the elimination method, it's often necessary to multiply one or both equations by a constant so that the coefficients of one of the variables are opposites. This ensures that the variable will be eliminated when you add the equations together.
🧠 Part A: Vocabulary
Match each term with its correct definition:
| Term |
Definition |
| 1. Linear System |
a. A value that, when substituted for a variable, makes the equation true. |
| 2. Variable |
b. A method for solving systems of equations by adding or subtracting equations to eliminate a variable. |
| 3. Solution |
c. A set of two or more linear equations containing the same variables. |
| 4. Coefficient |
d. A symbol (usually a letter) that represents an unknown value. |
| 5. Elimination Method |
e. The number that multiplies a variable in an algebraic expression. |
✏️ Part B: Fill in the Blanks
Complete the following paragraph with the correct terms:
To use the __________ method, you first need to make sure that one of the __________ has the same or opposite __________. If they don't, you can multiply one or both equations by a __________. Then, you either add or __________ the equations to eliminate one of the __________, leaving you with a single equation in one variable.
🤔 Part C: Critical Thinking
Explain, in your own words, why it's sometimes necessary to multiply one or both equations in a system of linear equations by a constant before using the elimination method. Provide an example to illustrate your explanation.