Unpacked Benchmarks
Benchmark: MA.912.A.3.13 - Use a graph to approximate the solution of a system of linear equations in two variables with and without technology.
Rewrite: Approximate the values for (x, y) where two or more linear equations intersect either by looking at a hand-drawn graph of the linear equations or by finding the point using a graphing calculator.
Essential Vocabulary: linear relationship, variable, system of linear equations, parallel, slope, intercepts, solution, intersection, ordered pairs.
Essential Questions: How would you describe a variable? How many different variables are used in this system (provide example) of equations? How do you know? Where do these linear equations intersect? Describe the solution set for these linear equations. What is the solution set for a system of linear equations that are all parallel to each other?
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Benchmark: MA.912.A.3.14 - Solve systems of linear equations and inequalities in two and three variables using graphical, substitution, and elimination methods. (Note – For the purposes of this lesson, we will not be covering inequalities.)
Rewrite: Find the point where two or more linear equations intersect by graphing the equations. Find the solution to two or more linear equations by isolating one variable and substituting it back into another equation. Find the solution to two or more linear equations by adding multiples of one equation to eliminate all but one variable, and then solving for the remaining variable, and repeating this process until all variables are found.
Essential Vocabulary: expression, linear equation, ordered pair, slope, coordinates, intersection, solution, variables, graphical, elimination, substitution
Essential Questions: If we use the substitution method, how do you know which expression to substitute into another equation? How would you isolate x in this equation? How would you isolate y? Does it matter how you isolate a variable? How can you use a graph to double-check a solution set found from either the substitution or elimination methods? How are the elimination and substitution methods similar to each other? Have students solve systems of linear equations using the elimination method, substitution method, and by graphical methods. Explain why they chose a particular method for each one.
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