Students create systems of equations that have the same solution set as a given system.
Students understand that adding a multiple of one equation to another creates a new system of two linear equations with the same solution set as the original system. This property provides a justification for a method to solve a system of two linear equations algebraically.
The sum of two numbers is 10 and their difference is 6. What are the numbers?
1. Create a system of two linear equations to represent this problem.
2. What is the solution to the system?
3. Create a new system of two linear equations using the methods described in question (9) of the Exploratory Challenge. Verify that the new system has the same solution.
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