Lesson 4: Solving by Elimination

When is it most efficient to use elimination versus other algebraic methods like substitution?  

How do you determine whether to add or subtract the equations to successfully eliminate a variable?  

What algebraic steps are required when neither variable has the same coefficient in both equations?

Elimination Method: A way to solve a system by adding or subtracting the equations to cancel out one of the variables.
Coefficient: The numerical factor of a variable term.
Additive Inverse: Two numbers that, when added together, result in zero (e.g., 3x and -3x).
System of Equations: A set of equations that are solved simultaneously.

8.EE.C.8.B: Solve systems of two linear equations in two variables algebraically.  

Target D.5: The student solves a system of two linear equations in two variables algebraically.

Description: In this lesson students will practice aligning equations and executing precise cancellations.  

Purpose: To provide a powerful alternative for systems where isolating a variable for substitution would result in complex fractions.

DOK Level: Level 2 (Basic Application) – Performing the mechanical steps of addition, subtraction, and multiplication for elimination.

Subtraction Errors: Forgetting to distribute a subtraction sign to every term in an equation, not just the first one.
Alignment Issues: Attempting to add or subtract equations when terms (x, y, = and constants) are not properly lined up.
Single Variable Stopping: Just like in substitution, students may forget to plug their first found value back into an original equation to find the second variable.

Support: Provide a "Vertical Alignment Organizer" that uses columns for x-terms, y-terms, and constants to prevent alignment errors.
Scaffolding: Start with "Direct Elimination" problems (where coefficients are already additive inverses) before moving to "Multiplication Required" problems.
Extension: Utilize the Systems of Equations Challenge Problems for advanced learners who can apply elimination to systems with non-integer coefficients.

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