Students are introduced to systems of linear equations and learn what it means for two equations to have a common solution. They explore graphical representations, identify different types of solutions, and develop an understanding of how intersecting, parallel, and coincident lines relate to the number of solutions.
Students learn efficient algebraic methods for solving systems of equations. They master substitution and elimination techniques, including systems requiring multiplication before elimination, and develop strategies for choosing the most appropriate solution method while checking the accuracy of their work.
Students investigate systems with no solution or infinitely many solutions and apply systems of equations to practical situations. They translate real-world problems into mathematical models involving variables, equations, and constraints.
Students extend their problem-solving skills to systems involving three variables. They learn systematic elimination techniques, solve more complex algebraic systems, use technology to verify solutions, and develop strategies for identifying and correcting common errors.
Students bring together all of the techniques learned throughout the course to solve authentic, multi-step problems. They build mathematical models for business, science, and geometry applications while evaluating the effectiveness and limitations of their models. The course concludes with integrated problem-solving activities that reinforce both conceptual understanding and procedural fluency.
Topics include:
Business and Economics
Science Applications
Geometry Applications
Mathematical Modelling
Review and Integrated Problem Solving
Course Outcomes
By the end of this course, students will be able to:
Understand what a system of equations represents and interpret its solutions.
Solve systems graphically, by substitution, and by elimination.
Identify systems with one solution, no solution, or infinitely many solutions.
Solve systems involving two and three variables.
Translate real-world situations into systems of equations.
Choose efficient solution methods for different types of problems.
Verify and communicate mathematical solutions accurately.
Apply systems of equations to problems in science, business, finance, geometry, and everyday life.
Develop mathematical models to analyze and solve complex real-world situations.
Build a strong foundation for future studies in functions, matrices, linear algebra, calculus, and advanced mathematical modelling.