Open Middle®
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?
Answer
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
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 🙂
thank you so much that help me a lot.
4x+2y=16
6x+y=20
This a problem that would motivate my students. They would be competing to see who could find more solutions.
This problem will engage students and help them have a deeper understanding of the concept.
The exploration in this problem will motivate to students to learn.
This problem is great, but everyone’s answers could mean students look up solutions instead of finding them. I added a twist to make it both individual and harder to just look up answers.
I have a set of 10-sided dice. I made the students roll two, different color dice and the results became the solution for the lines. Since an infinite amount of lines exist through any one point, there should still be the same number of possible system of equations as picking the solution (3,2).