Adaptive Perseverance: Students will persist in solving complex systems of equations despite challenges, exploring multiple methods for optimal solutions.
Learner’s Mindset: Students will demonstrate curiosity and a willingness to explore different solving methods, seeking continuous improvement.
Communication: Students will articulate their problem-solving process clearly, both verbally and in writing, for various methods.
Global Citizenship: Students will understand the relevance of solving complex systems in real-world applications, recognizing its importance in various fields.
Critical Thinking: Students will analyze and evaluate different methods for solving systems, applying logical reasoning to select and justify their approach.
Collaboration: Students will work together to solve complex systems, leveraging each other's strengths and perspectives for effective solutions.
What are the advantages and disadvantages of solving systems of linear equations using graphing, substitution, and elimination methods?
How can we determine the most efficient method to solve a given system of linear equations?
How do the techniques used for solving systems of two equations and two unknowns extend to systems with three equations and three unknowns?
Students are able to convert quantitative problems that use words into mathematical expressions.
CCCSS.MATH.CONTENT.HSA.REI.C.5: Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions.
CCSS.MATH.CONTENT.HSA.REI.C.6: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.
CCSS.MATH.CONTENT.HSA.REI.C.7: Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically.
CCSS.MATH.CONTENT.HSA.REI.C.8: Represent a system of linear equations as a single matrix equation in a vector variable.
CCSS.MATH.CONTENT.HSA.REI.C.9: Find the inverse of a matrix if it exists and use it to solve systems of linear equations.
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