This document discusses special types of linear systems and asks the reader to predict, graph, and analyze the solutions to 4 different systems of linear equations. For each system, the reader is asked to predict whether the system will have no solution, a unique solution, or infinitely many solutions based on the graphs of the lines, graph the system in Desmos, and then reflect on whether their initial prediction was correct or not.

1. Special Types of Linear Systems
Name: ____________________ Date: __________
Put the following linear systems into Desmos and answer the questions below.
1) y = -2x + 3
y = -2x + 5
PREDICT: What type of solution do you think this system will have? Why?
Graph: Sketch what the graphs looked like:
React: Were you correct?
2) y = 4x – 3
y = 2x + 4
PREDICT: What type of solution do you think this system will have? Why?
Graph: Sketch what the graphs looked like:
React: Were you correct? Why do you think the graph looked this way?

2. 3) y = -x + 5
y = ½ x + 5
PREDICT: What type of solution do you think this system will have? Why?
Graph: Sketch what the graphs looked like:
React: Were you correct?
4) 2x + y = 5
x + 2y = 8
PREDICT: What type of solution do you think this system will have? Why?
Graph: Sketch what the graphs looked like:
React: Were you correct?