Solving Systems by Elimination Worksheets for Grade 8 (with Answer Key)

📚 Topic Summary

Solving systems of equations by elimination is a method used to find the solution (the values of the variables) that satisfies two or more equations simultaneously. The main idea is to manipulate the equations so that when you add or subtract them, one of the variables cancels out. This leaves you with a single equation in one variable, which you can then solve. After finding the value of one variable, you can substitute it back into either of the original equations to find the value of the other variable.

For Grade 8, we'll focus on simple systems of two linear equations with two variables. Make sure the coefficients of one of the variables are either the same or opposites, so they cancel when you add or subtract the equations.

🧠 Part A: Vocabulary

Match each term to its correct definition:

1. System of Equations
2. Elimination
3. Coefficient
4. Variable
5. Solution

Definitions:

1. A symbol (usually a letter) that represents an unknown value.
2. A set of two or more equations containing the same variables.
3. The process of removing a variable by adding or subtracting equations.
4. A value that, when substituted for a variable, makes an equation true.
5. A number multiplied by a variable in an algebraic expression.

📝 Part B: Fill in the Blanks

Complete the following paragraph with the correct words:

To solve a system of equations by __________, we aim to __________ one of the __________. This is done by adding or __________ the equations together. The goal is to get an equation with only one __________, which we can then solve. Finally, we __________ the value we found back into one of the original equations to find the value of the other variable.

Possible words: variable, elimination, subtract, eliminate, substitute

Solution: To solve a system of equations by elimination, we aim to eliminate one of the variables. This is done by adding or subtract the equations together. The goal is to get an equation with only one variable, which we can then solve. Finally, we substitute the value we found back into one of the original equations to find the value of the other variable.

💡 Part C: Critical Thinking

Explain in your own words why it's important to make sure the coefficients of one of the variables are opposites or the same before you add or subtract the equations when using the elimination method. Give an example to illustrate your point.

(Answer: If the coefficients are not opposites or the same, simply adding or subtracting the equations will not eliminate any variable, and you will not be able to solve for either variable directly. Example: Consider the equations $x + y = 5$ and $2x + y = 8$. If you simply add them, you get $3x + 2y = 13$, which still has two variables. To eliminate y, you could subtract the first equation from the second to get $x = 3$.)