Solving Systems Guided Notes

[Jennell Venier]

Inthis lesson plan, students will learn about solving system of equations, also known as simultaneous equations, and their real-life applications. Through artistic, interactive guided notes, check for understanding, practice coloring by code, and a maze worksheet, students will gain a comprehensive understanding of system of equations by graphing.

As a hook, ask students why understanding how to solve a system of linear equations by graphing is important in real-life situations. Refer to the last page of the guided notes as well as the FAQs below for ideas.

Use the first page of the guided notes to introduce the concept of solving a system of two linear equations by graphing. Identify cases of graphs of system of linear equations with one solution (intersection), no solution (parallel lines) or infinite solutions (overlapping lines). Then, walk through the steps involved in graphing each equation on the coordinate plane and finding the point of intersection (in the case of one solution).

Repeat the instruction for the second page of the guided notes. Students are provided with practice examples of pairs of linear equations through graphing. Ensure students understand the relationship between the graph and the solution.

Based on student responses, reteach concepts that students need extra help with regarding graphing linear equations and finding solutions. If your class has a wide range of proficiency levels, consider pulling out students for reteaching while more advanced students start working on the practice exercises.

Have students practice solving systems of linear equations by graphing using the practice worksheet included in the resource (pg. 2) as well as the maze activity (pg. 3), and color by number worksheets (pg. 4). Monitor the class as they work through the problems and offer assistance as needed.

Using the last page of the guided notes (pg. 5), bring the class back together, and introduce the concept of using system of equations by graphing to analyze scenarios in the real world where multiple linear relationships intersect.

This could involve situations like determining the break-even point for a business, analyzing the intersection of supply and demand curves in economics, or understanding the point of equilibrium in physics problems.

The proof system of Dual-Rail MaxSAT (DRMaxSAT) was recently shown to be capable of efficiently refuting families of formulas that are well-known to be hard for resolution, concretely when the MaxSAT solving approach is either MaxSAT resolution or core-guided algorithms. Moreover, DRMaxSAT based on MaxSAT resolution was shown to be stronger than general resolution. Nevertheless, existing experimental evidence indicates that the use of MaxSAT algorithms based on the computation of minimum hitting sets (MHSes), i.e. MaxHS-like algorithms, are as effective, and often more effective, than core-guided algorithms and algorithms based on MaxSAT resolution. This paper investigates the use of MaxHS-like algorithms in the DRMaxSAT proof system. Concretely, the paper proves that the propositional encoding of the pigenonhole and doubled pigenonhole principles have polynomial time refutations when the DRMaxSAT proof system uses a MaxHS-like algorithm.

N2 - The proof system of Dual-Rail MaxSAT (DRMaxSAT) was recently shown to be capable of efficiently refuting families of formulas that are well-known to be hard for resolution, concretely when the MaxSAT solving approach is either MaxSAT resolution or core-guided algorithms. Moreover, DRMaxSAT based on MaxSAT resolution was shown to be stronger than general resolution. Nevertheless, existing experimental evidence indicates that the use of MaxSAT algorithms based on the computation of minimum hitting sets (MHSes), i.e. MaxHS-like algorithms, are as effective, and often more effective, than core-guided algorithms and algorithms based on MaxSAT resolution. This paper investigates the use of MaxHS-like algorithms in the DRMaxSAT proof system. Concretely, the paper proves that the propositional encoding of the pigenonhole and doubled pigenonhole principles have polynomial time refutations when the DRMaxSAT proof system uses a MaxHS-like algorithm.

AB - The proof system of Dual-Rail MaxSAT (DRMaxSAT) was recently shown to be capable of efficiently refuting families of formulas that are well-known to be hard for resolution, concretely when the MaxSAT solving approach is either MaxSAT resolution or core-guided algorithms. Moreover, DRMaxSAT based on MaxSAT resolution was shown to be stronger than general resolution. Nevertheless, existing experimental evidence indicates that the use of MaxSAT algorithms based on the computation of minimum hitting sets (MHSes), i.e. MaxHS-like algorithms, are as effective, and often more effective, than core-guided algorithms and algorithms based on MaxSAT resolution. This paper investigates the use of MaxHS-like algorithms in the DRMaxSAT proof system. Concretely, the paper proves that the propositional encoding of the pigenonhole and doubled pigenonhole principles have polynomial time refutations when the DRMaxSAT proof system uses a MaxHS-like algorithm.

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Expository classes in large group: They will consist of masterclasses of the program content for the whole group. The contentswill be developed and discussed. Problems and exercises proposed bythe teacher will be solved. This methodology and activitieswill allow students to acquire the indicated competencies (CB2R,CB3R, CB5R, CEM7).

Small group classes: Practices will be held in the laboratorywhere the student will receive guided notes with the objectives ofeach test and the procedure to follow for its development. Thestudent must take note of the experimental data necessary to carryout the corresponding calculations and be able to make a correctpractical report. Computer practices will be carried out withspecific Material Selection software. In addition exercises will besolved, exhibitions and other practical activities will beheld for students to develop the CEM7 competence (Knowledgeand skills for the application of materials engineering)

Purpose: In accordance with the Universities Law and other national and regional regulations in force, carrying out exams and assessment tests corresponding to the courses students are registered in. In order to avoid frauds while sitting the exam, the exam will be answered using a videoconference system, being able the academic staff of the University of Jan to compare and contrast the image of the person who is answering the exam with the student's photographic files. Likewise, in order to provide the exam with evidential content for revisions or claims, in accordance with current regulation frameworks, the exam will be recorded and stored.

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This section sets out why studying this programme is important, both in terms of inspiring you as an individual and in considering the challenges we face. It describes how this degree programme contributes to:

The programme will produce graduates who have a good theoretical and practical understanding of the technologies involved in electro-mechanical energy conversion systems. This will embrace aspects from the:

An underpinning thread will be to understand the interactions between the electrical and mechanical system, and theory behind the components that make up electro-mechanical energy conversion system including function, analysis, dynamic behaviour and control.

Graduating students will be equipped to straddle the disciplines of electrical and mechanical engineering. They will understand the differences and synergies between the fundamental energy conversion, energy storage and dynamical behaviours of the two domains. For example a typical graduate would:

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