Lesson 10: Systems of Linear Equations and Their Solutions (Alg1.2.17)
Math TalkWhat do you notice? What do you wonder?
A Curious SystemAndre is trying to solve this system of equations:
Looking at the first equation, he thought, "The solution to the system is a pair of numbers that add up to 3. I wonder which two numbers they are." Choose any two numbers that add up to 3. Let the first one be the -value and the second one be the -value.
The pair of values you chose is a solution to the first equation. Check if it is also a solution to the second equation. Then, pause for a brief discussion with your group.
How many solutions does the system have? Use what you know about equations or about solving systems to show that you are right.
Sorting SystemsEach card contains a system of equations. Sort the systems into three groups based on the number of solutions each system has. Be prepared to explain how you know where each system belongs.
Are you ready for more?Here is an equation:
Create a second equation that would make a system of equations with one solution.
Create a second equation that would make a system of equations with no solutions.
Create a second equation that would make a system of equations with infinitely many solutions.