Lesson 2: Solving Systems by Graphing

• How do we solve a system by graphing?
• What does the intersection point represent?
• What if the lines don't intersect?
• What if the lines are the same?

Graph, intersection, solution, parallel, coincident, one solution, no solution, infinite solutions

CCSS.MATH.8.EE.C.8

Description: Students graph both equations on the same coordinate plane and find where they intersect. The intersection point is the solution. They explore three cases: one intersection (one solution), parallel lines (no solution), and identical lines (infinite solutions). Purpose: To develop visual understanding of systems and their solutions. DOK Level: 2-3 (Application)

• Start with simple equations: y = x + 1 and y = -x + 3
• For struggling learners: Provide tables for graphing; focus on finding intersection
• For advanced learners: Explore all three cases (one, none, infinite solutions)
• Graphing technology: Use Desmos for visualization

• Observation: Can students graph linear equations correctly?

• Worksheet: Graph two equations and identify their intersection

• Verification: Check the solution in both equations

• Exploration: Graph systems with different numbers of solutions

• System graphing worksheets

• Input/output table templates

• Coordinate plane worksheets

• Graphing technology (Desmos)

• Resource: Khan Academy "Solving Systems by Graphing" (adapted)