 # Create a System of Two Equations

Directions: Using the digits 1 to 30, at most one time each, fill in the boxes to create a system of two linear equations where (3, 2) is the solution to the system. ### Hint

What does it mean to be the solution to a system of linear equations?

Many possible correct responses. For example:

3x + 5y = 19
4x + 1y = 14

For more solutions see https://www.desmos.com/calculator/clsixz0vom (courtesy of Colleen Young)

Source: Daniel Luevanos

## Difference of Squares and Sum of Cubes

Directions: Using the digits 0 to 9 at most one time each, place a digit …

1. What a wonderful problem – thank you. I could not resist a play with Desmos to generate more solutions!
https://www.desmos.com/calculator/clsixz0vom

• Thanks for this Colleen. I have added it to the answer 🙂

2. thank you so much that help me a lot.

3. 4. This a problem that would motivate my students. They would be competing to see who could find more solutions.

5. This problem will engage students and help them have a deeper understanding of the concept.

6. The exploration in this problem will motivate to students to learn.