[size=150][math]\begin {cases} x + y = 3\\ 4x = 12 - 4y \end{cases}[/math][/size][br][br][size=150]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."[/size] [br][br]Choose any two numbers that add up to 3. Let the first one be the [math]x[/math]-value and the second one be the [math]y[/math]-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.[br]
How many solutions does the system have? Use what you know about equations or about solving systems to show that you are right.
[size=150]On the first day of the offering, a family paid $96 for 4 pool passes and 2 gym memberships. Later that day, an individual bought a pool pass for herself, a pool pass for a friend, and 1 gym membership. She paid $72. [/size][br][br]Write a system of equations that represents the relationships between pool passes, gym memberships, and the costs. Be sure to state what each variable represents.
Find the price of a pool pass and the price of a gym membership by solving the system algebraically. Explain your reasoning.[br]
Use graphing technology to graph the equations in the system. Make 1-2 observations about your graphs.[br]
In the cards, for each system with no solution, change a single constant term so that there are infinitely many solutions to the system.
For each system with infinitely many solutions, change a single constant term so that there are no solutions to the system.
Explain why in these situations it is impossible to change a single constant term so that there is exactly one solution to the system.[br]
[math]5x-2y=10[/math][br][br]Create a second equation that would make a system of equations with one solution.[br]
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.