Solving Systems of Linear Equations Chapter 7 (Sections 7.1 - 7.5) Alberta Grade 10 Math Review

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Summary of Chapter 7: Systems of Linear Equations
Core Concepts
Introduction: A system of linear equations consists of two or more linear equations involving the same set of variables. The solution is a set of values that satisfies all equations simultaneously.
Sections Overview
Section 7.1: Developing Systems of Linear Equations
Focuses on creating systems from real-world scenarios. For example, a school with buses of different capacities can be modeled with equations. Each unknown variable requires an equation, leading to a system for two unknowns.
Section 7.2: Solving Systems by Graphing
Introduces graphing as a method to solve systems. Each equation is converted to slope-intercept form, and the intersection point of the graphs represents the solution. This method is intuitive but can be time-consuming and yield approximate results.
Section 7.3: Using Technology for Graphing
Utilizes graphing calculators to input equations, speeding up the process while still providing approximate solutions. This method is effective for complex equations.
Section 7.4: Substitution Method
Focuses on the substitution method, where one equation is solved for a variable and substituted into the other. This method simplifies the solving process compared to graphing. For instance, solving the system2x+3y=12 and x-y=2 leads to y=2 and x=4.
Section 7.5: Elimination Method
Introduces the elimination method, which involves adjusting equations to eliminate one variable, allowing for easier solving of the remaining variable. This method is effective when coefficients are structured for easy cancellation. An example demonstrates how to align equations for elimination.
Practical Applications
Systems of linear equations are crucial in fields like economics and engineering, helping model real-world scenarios such as capacities or costs. Understanding how to identify variables and create equations based on relationships is essential for solving practical problems.
Conclusion
The chapter covers essential techniques for solving systems of linear equations, including graphing, substitution, and elimination methods. Each method has its advantages, with algebraic methods generally preferred for their precision.
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