Open Middle®
Directions: Write at least two linear equations so that the solution of the system of equations of that line and 4x + y = 8 is (3, -4)
Hint
What does it mean to be a solution of a system of equations?
A modification for this problem could be that the solution to a system is (0, -5). Students are to create a system of equations that has (0, -5) as the solution.
Another modification could be using Desmos. Here is a link to the problem I graphed using Desmos.
Answer
There are many linear equations that meet the constraints. Here are a couple of solutions.
y = x – 7
2x + 3 y = -6
y = x – 7
2x + 3 y = -6
Source: Nanette Johnson
For high school ( or adavnced) push them with the extension, is it possible to show all possibilities? Shows value in point-slope and use of variables.
y + 4 = a(x – 3) where a cannot equal -4.
Just a thought to an already great problem! Used it today. Nice work!
I always like the “outside the box” thinkers in my class:
y= – 4
x = 3
Change the directions to two equations with two variables each…
Larry : Love your extension.
y=x-1
2x+2y=18
(4,5)