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Course Title: Algebra 1 Grade: Essential Questions: Pace: 1. The graphs of the systems of two linear equations in two variables can show the number of solutions to the system. 2. Systems of equations in two variables can be solved using graphing, substitution, or elimination (linear combinations). 3. The solution to a system of linear inequalities is the region of intersection of “Half-Planes”. 4. Parallel lines indicate no solutions, overlapping lines (Equivalent lines) indicate infinite solutions, and non-parallel lines indicate one solution to a system of linear equations. Content – Unit Focus Standards/ Framework Learning Targets Systems of Equations/Inequalities A.CED.3 Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods. Write and solve a system of linear equations/inequalities that represent a realworld situation. A.REI.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. Use graphing method to solve a system of linear equations. A.REI.6 Solve systems of linear equations exactly and approximately Use substitution method to solve a system of linear equations. Resources Assessments (e.g., with graphs), focusing on pairs of linear equations in two variables. Use elimination to solve a system of linear equations. A.REI.11 Explain why the xcoordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.★ A.REI.12 Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. Use graphing to solve a system of linear inequalities.