Practice solving liner systems using different methods and multiple representations. In each of the eight tasks, students will interpret a given story and then create a system of equations, two tables of values, and a graph. Finally, students solve the system algebraically.
These tasks allow students of all ability levels to understand systems. Some students can jump right into the algebra of it all. Others need to see the graph. And some like to build the tables to see when the values match. All three methods are useful and can generate a solution.
The tasks range in difficulty, so they can be used for differentiation. They could be used for classwork practice, group work, bell ringers, exit tickets, centers, or assessments. Six of the tasks have one intersection and one solution. Two tasks have no solution (parallel lines). All of these systems can be solved with substitution.
You will receive PDFs of the 8 tasks (one-page each) and the 8 answer keys.
Common Core Standards
Analyze and solve pairs of simultaneous linear equations.
Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously.
Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. For example, 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6.
Solve real-world and mathematical problems leading to two linear equations in two variables. For example, given coordinates for two pairs of points, determine whether the line through the first pair of points intersects the line through the second pair.
Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.
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