Lesson 3: Types of Solutions
Duration of Days: 2
Lesson Objective
Students will recognize and identify when a system of two linear equations has one solution, no solution, or infinitely many solutions.
Students will identify these solution types through inspection and by analyzing the relationship between slopes and y-intercepts
How can we tell if two lines will never intersect just by looking at their equations?
What does it mean for a system to have infinitely many solutions visually and algebraically?
Why can 3x+2y=5 and 3x+2y=6 never have a common solution?
One Solution, No Solution, Infinitely Many Solutions, Parallel Lines, Coinciding Lines, Slope, y-intercept
8.EE.C.8: Analyze and solve pairs of simultaneous linear equations.
8.EE.C.8b: Solve simple cases by inspection (e.g., recognizing parallel lines with different intercepts as having no solution).
Purpose: To move beyond finding a single intersection point and understand the three possible outcomes of a linear system.
DOK Level: 3 (Strategic Thinking).
Students may interpret an algebraic result of a=a (like 5=5) as the solution being "a" rather than recognizing it means infinitely many solutions.
Students may interpret a result of a=b (like 0=7) as the solution being 0 rather than recognizing it means no solution.
Provide visual comparison charts showing parallel, intersecting, and overlapping lines alongside their equations.
Provide sentence starters to help students explain their reasoning for a specific solution type.
Exit Ticket
Student Self Assessment