Create a System of Equations, Given 1 Equation and the Solution

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)


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.


There are many linear equations that meet the constraints. Here are a couple of solutions.
y = x – 7
2x + 3 y = -6

Source: Nanette Johnson

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  1. 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!

  2. 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.

  3. y=x-1

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