Students begin by comparing the constant speed of two individuals to determine which has greater speed. Students graph simultaneous linear equations to find the point of intersection and then verify that the point of intersection is in fact a solution to each equation in the system. To motivate the need to solve systems algebraically, students graph systems of linear equations whose solutions do not have integer coordinates. Students use an estimation of the solution from the graph to verify their algebraic solution is correct.
Students learn to solve systems of linear equations by substitution and elimination. Students understand that a system can have a unique solution, no solution, or infinitely many solutions, as they did with linear equations in one variable. Finally, students apply their knowledge of systems to solve problems in real-world contexts, including converting temperatures from Celsius to Fahrenheit.
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