Hey everyone,
I wanted to share something interesting I’ve noticed about solving systems of linear equations. It all comes down to what happens when you look at the equations together:
Infinite Solutions: If two equations look the same on both sides , they’re basically describing the same line. That means there are infinite points that satisfy both equations. So, the system has infinitely many solutions.
- Unique Solution: When you slightly tweak the coefficients on the left side (like changing the multiplier of ‘x’ or ‘y’), you might make the two lines cross at exactly one point. This crossing point is the unique solution to the system. So in this case, there’s one unique solution.
No Solution: But if you change just the number on the right side (without touching the left side), you might end up with parallel lines that never meet. This means there’s no point that works for both equations at the same time, so the system has no solution.
I hope this helps make sense of how different tweaks in the equations can change the number of solutions you get!