Ms. Terkper's Digital Classroom

Unit 10: Systems of Linear Equations (Math 10C)

Solve by graphing, substitution, and elimination; classify number of solutions; apply to real problems.

Graphing Substitution Elimination One / None / Infinite Solutions Applications

What You Should Be Able To Do

  • Solve a system by graphing and interpret the intersection point.
  • Solve by substitution and by elimination; check solutions.
  • Recognize no solution (parallel), infinite solutions (coincident), or one solution (intersecting).
  • Model and solve applications (price/ticket, mixture, motion, etc.).

Quick Reminders

  • Graphing: intersection \((x,y)\) satisfies both lines.
  • Substitution: solve one equation for a variable, substitute in the other.
  • Elimination: line up like terms, multiply if needed, add/subtract to eliminate a variable.

Video Library

Solve by Graphing

Plot both lines; read intersection.

Substitution Method

Isolate a variable, plug into the other equation.

Elimination Method

Multiply and add/subtract to eliminate a variable.

Applications

Translate contexts to equations.

Interactive Tools

System Grapher & Classifier (General Form \(Ax+By=C\))

Solve by Substitution (Step-by-Step)

Elimination & Applications

Solve by Elimination (Step-by-Step)

Applications Builder (Create a System)

Unit 10 Quizzes

Quiz 1: Graphing & Substitution

Find intersections and check solutions.

Quiz 2: Elimination & Applications

Multiple representations and word problems.

Downloadable Review

Download PDF

Quick Practice Scratchpad

Try: Solve \(\begin{cases}3x-2y=7\\x+y=5\end{cases}\). Classify \(\begin{cases}2x-4y=8\\x-2y=5\end{cases}\). Write a system for: “Adult t-shirts \$18, youth \$12, sold 110 shirts for \$1680.”