Systems of Three Equations – Multiple Solutions

Directions: Using the digits 1 through 9, at most one time each, create a system of equations that has as many solutions as possible.

Hint

How would three lines that have one solution look on a graph?  How would three lines that have two solutions look on a graph?  How would three lines that have three solutions look on a graph?  How would three lines that have more than 3 solutions look on a graph?

Answer

To have an infinite number of solutions, they would have to be three identical lines. So, one possible answer is 4x + 8y = 0, 3x + 6y = 0, and 1x + 2y = 0 which gives three identical lines.

Source: Audrey Mendivil, Daniel Luevanos, and Robert Kaplinsky

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