Systems of Three Equations – No Solution

Directions: Using the digits 1 through 9, at most one time each, create a system of equations that has no solutions.


What would three lines on a plane that do not intersect look like?


There are multiple answers but the lines must be parallel.  One solution is 1x + 2y = 5, 3x + 6y = 7, 4x + 8y = 9

Source: Nanette Johnson and Robert Kaplinsky

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  1. Thanks for the problem! Am I overlooking something? The way I am thinking of it, a system of 3 equations and two unknowns has a solution only if all three lines intersect at a common point. Three lines with different slopes might probably don’t do this.

    1x + 2y =9
    4x + 6y = 5
    7x + 8y = 3

    Have no common point of intersection

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