Lesson 4: Substitution Method
Duration of Days: 2
Lesson Objective
Students will solve systems of two linear equations in two variables algebraically using the substitution method.
Students will recognize when one equation is already solved for a variable and use that expression to find the value of the second variable.
Why is it sometimes more effective to solve a system algebraically rather than by graphing?
How does "replacing" a variable with an equivalent expression help us solve for a single unknown?
What does it mean for a system to have no solution or infinite solutions when solving algebraically?
Substitution, Algebraic Solution, Variable, Coefficient, Distributive Property, Like Terms, Replace
8.EE.C.8b: Solve systems of two linear equations in two variables algebraically.
8.EE.C.8c: Solve real-world and mathematical problems leading to two linear equations in two variables.
Purpose: To introduce a precise algebraic tool for finding intersection points, especially when solutions involve fractions or decimals that are difficult to see on a graph.
DOK Level: 2 (Skill/Concept) and 3 (Strategic Thinking).
Distribution Errors: Students may forget to distribute a coefficient to both terms in the expression.
Variable Confusion: Students might substitute an expression for the wrong variable.
Incomplete Solutions: Students may find the value of one variable and forget to substitute it back in to find the second coordinate of the ordered pair.
Provide a step-by-step checklist (1. Isolate, 2. Substitute, 3. Solve, 4. Plug-back).
Use color-coded examples where the "substituted" expression is highlighted to show where it moves.
Offer practice problems where one variable is already isolated.
Exit Ticket
Student Work