Interactive resource
Linear Systems: Intersection of Two Lines
Algebra. Adjust two line equations and see unique, none, or infinitely many solutions as intersection, parallel, or coincident lines. Free interactive…
Overview
A solution of a 2×2 linear system is where two lines meet. Parallel means none; coincident means infinitely many.
Explanation
For a₁x+b₁y=c₁ and a₂x+b₂y=c₂, solutions are intersection points of two lines.
Intersecting: unique solution; parallel: none; coincident: infinitely many.
Solve by elimination or substitution.
How to use
- Open the linear-system scene.
- Change coefficients of both lines.
- Read the intersection coordinates.
- Try making the lines parallel or coincident.
Class prompt
Ask how to change coefficients to force parallel lines, then let students try.
Knowledge points
FAQ
How does this relate to substitution?
Algebra finds the intersection; this tool builds the geometric picture first.
Is this tool free?
Yes. It runs in the browser with no install.
Good for class demos?
Yes — project it and ask what changes when you drag a parameter.
How do I write the formula afterward?
Open the equation editor or symbol sheet and copy a clean expression.