Think of or draw an interesting pattern made of at least 4 lines.

Write at least 4 linear equations to create your pattern with these conditions:

• At least one equation written in standard form: with constants for and .
• At least one equation written in slope-intercept form: with constants for and .
• At least 2 lines that intersect.
• At least 2 lines that do not intersect.

Trade equations with your new partner. Only the equations should be traded. Do not trade the patterns yet.

1. Create a system of equations by selecting two of the equations that your partner gave you. Without graphing, solve that system of equations or show why there are no solutions. Be prepared to show your reasoning.
2. Select another pair of equations, and do this again.
3. Using one of the equations you have, write a new linear equation to create a system that has infinitely many solutions.
4. Next, you and your partner should show each other your original patterns and check your answers using those graphs.