Sections from the Glencoe Algebra I Textbook:

Systems of Equations: 6.1, 6.2, 6.3, 6.4, 6.5

Systems of Inequalities: 5.6, 6.6

Discovery Ed. Lessons 5.1 & 5.2

Unit Objectives:

• Solve systems of linear equations graphically and algebraically.
• Solve systems of inequalities graphically.
• Strategically convert between various forms for a linear equation, depending on the situation.
• Use graphical representations of inequalities to interpret constraints.
• Use systems of inequalities to represent real-world situations involving constraints.
• Interpret and solve systems of inequalities involving constraints.
• Graph systems of equations and inequalities

New Jersey Student Learning Standards for this Unit:

• A.CED.A.2: Create equations in two or more variables to represent relationships between quantities: graph equations on coordinate axes with labels and scales.
• A.CED.A.3: Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods.
• A.CED.A.4: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm’s law V=IR to highlight resistance, R.
• A.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 nonzero multiple of the other produces a system with the same solutions.
• A.REI.C.6: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.
• A.REI.D.11: Explain why the x-coordinates 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.D.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.
• N.Q.A.3: Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.