Grade 8 Intro to Systems of Linear Equations Practice Sheets

📚 Topic Summary

Systems of linear equations are a set of two or more linear equations containing the same variables. The "solution" to a system is the point (or points!) where the lines intersect, meaning the values for the variables that make all equations true simultaneously. Think of it as finding where two or more lines cross paths on a graph. This point satisfies all equations in the system.

In 8th grade, you'll primarily focus on solving systems graphically or using substitution. Graphing involves plotting the lines and finding the intersection. Substitution involves solving one equation for one variable and then substituting that expression into the other equation. Let's dive into some practice!

🔤 Part A: Vocabulary

Match the term to its definition:

1. Term: System of Equations
2. Term: Linear Equation
3. Term: Solution
4. Term: Variable
5. Term: Intersection

1. Definition: A symbol (usually a letter) that represents a value that can change.
2. Definition: A set of two or more equations containing the same variables.
3. Definition: The point where two or more lines or curves meet.
4. Definition: An equation whose graph is a straight line.
5. Definition: A value or set of values that makes an equation or system of equations true.

✍️ Part B: Fill in the Blanks

A ________ of linear equations involves two or more linear equations using the same ________. A ________ to the system is a set of values that satisfy ________ the equations. When graphing, this is the point of ________.

1. Options: system, variables, solution, all, intersection

🤔 Part C: Critical Thinking

Explain in your own words why understanding systems of linear equations might be useful in real-world situations.