Lesson 3: Solving by Substitution

When is it more efficient to use substitution instead of graphing to solve a system?  

How does replacing a variable with an equivalent expression help us find a numerical solution for a system?  

What algebraic steps are required to "check" if a solution found through substitution is correct?

Substitution Method: An algebraic way to solve a system of equations by replacing one variable with an equivalent expression from the other equation.  

Equivalent Expression: An algebraic expression that has the same value as another for any value of the variables.  

Variable Isolation: The process of rearranging an equation so that one variable is alone on one side.  

Exact Solution: A numerical value that satisfies the system perfectly, rather than an estimate from a graph.  

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: This lesson transitions students from estimation to exact algebraic calculation.

Purpose: To provide students with a reliable method for finding solutions when graphs are not easily readable or when precision is required.

DOK Level: Level 2 (Basic Application) – Performing algebraic steps for substitution.

Incomplete Substitution: Forgetting to substitute the entire expression (e.g., substituting only the coefficient) into the second equation
.Distributive Property Errors: Failing to distribute correctly when a variable being replaced has a coefficient in the target equation.
Single Variable Stopping: Finding the value for one variable (like x) and assuming the problem is complete without finding the second variable ($).

Support: Provide a "Step-by-Step Substitution Checklist" to help students track their progress through the algebraic process.  

Scaffolding: Provide low-stakes practice with immediate peer feedback.  

Exit Tickets