1. Graph Interpretation
The system of equations below is graphed on the xy-plane. What does the point of intersection represent in the context of the system?
2. No Solution Identification
Does this system have one solution, infinite solutions, or no solutions? How can you tell without graphing or algebraically solving?
y = 3x+5
y = 3x−2
3. SAT Application
A gym offers two membership plans. Plan A charges a $40 sign-up fee plus $15 per month. Plan B charges no sign-up fee but costs $25 per month. After how many months will the total cost of both plans be the same?
4. Method Selection
Solve the following system of equations using the method you believe is most efficient:
2x + y = 11
x - y = 1
Explain why you selected that method.