📚 Topic Summary
The elimination method is a technique used to solve systems of equations. When the coefficients of one variable don't directly match (e.g., $2x$ and $3x$), you can multiply one or both equations by a constant so that the coefficients of either $x$ or $y$ are opposites or equal. This allows you to eliminate that variable by adding or subtracting the equations. For instance, to solve for $x$ and $y$ in a system like $\begin{cases} 2x + y = 5 \ x - 3y = -8 \end{cases}$, you might multiply the second equation by -2 to eliminate x.
This worksheet will give you a chance to practice these skills so you will be solving systems of equations like a pro. Here we go!💪
🧮 Part A: Vocabulary
Match the terms on the left with their definitions on the right:
| Term |
Definition |
| 1. System of Equations |
A. A method to solve systems by adding or subtracting equations |
| 2. Elimination Method |
B. Changing the form of an equation without changing its solution |
| 3. Coefficient |
C. A set of two or more equations with the same variables |
| 4. Variable |
D. A symbol representing an unknown value |
| 5. Equivalent Equations |
E. The number multiplied by a variable |
Match the correct numbers and letters in your notebook!
✍️ Part B: Fill in the Blanks
Use the words from the box below to complete the paragraph.
Words: multiply, eliminate, opposite, equation, constant
To use the elimination method effectively, you might need to ______ one or both equations by a ______. This is done to make the coefficients of one variable _______ or equal. Then, you can add or subtract the _______ to _______ that variable and solve for the remaining one.
🤔 Part C: Critical Thinking
Explain, in your own words, why multiplying one or both equations in a system by a constant doesn't change the solution to the system. Use an example to illustrate your explanation.