Two-by-Two Linear Systems Problem Generator

Drag the locators to move the lines. Each locator snaps to the nearest point with integer coordinates. The equations of the lines are displayed on the right as a two-by-two system of linear equations with integer coefficients. Provided that a unique solution exists, it will be displayed as well (the solution is the point of intersection of the two lines).
It is not hard to position the lines in such a way that the solution will also be a point with integer coordinates. This Demonstration can be used to generate thousands of such examples. Mathematics instructors can use it as a simple tool for creating problems for beginning students.
You can also use it to challenge more advanced students; for example, among all systems that can be generated here whose solution has integer coordinates, can you find one whose solution is farthest from the origin?

THINGS TO TRY

SNAPSHOTS

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DETAILS

The three constants appearing in each equation will contain no common factor other than 1.
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Related Curriculum Standards

US Common Core State Standards, Mathematics