Warm Up
Andre 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.
Compare your answer: Your answer may vary, but here are some samples.
4 and , 0 and 3, and
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.
Compare your answer: Your answer may vary, but here is a sample.
Yes, it is also a solution to the second equation. Sample reasoning for 4 and -1: Substituting 4 and -1 into the second equation gives or , which is a true equation.
How many solutions does the system have? Use what you know about equations and solving systems to show that you are right.
Compare your answer:
Infinitely many solutions