This Warm-up reminds students about the fact that some systems of linear equations have many solutions, while also prompting them to use what they learned in this unit to better understand what it means for a system to have infinitely many solutions.

The first equation shows two variables adding up to 5, so students choose a pair of values whose sum is 5. They notice that all pairs chosen are solutions to the system. Next, they try to find a strategy that can show that there are countless other pairs that also satisfy the constraints in the system. Monitor for these likely strategies:

• Solving by graphing: The graphs of the two equations are the same line, so all the points on the line are solutions to the system.
• Solving by substitution: The first equation can be rearranged to . Substituting for in the second equation gives , or