Systems of Equations
📋 What it is
A system is two equations with two unknowns; the solution is the point where both are true at once.
🗣️ Coach says
Sometimes one equation isn't enough to pin down two unknowns — you need two. The solution is the pair (x, y) that satisfies BOTH. Graphically, it's where the two lines cross.
🧠 Memory hook
Two unknowns need two equations. The answer makes BOTH true — where the lines cross.
😂 Giggle
Why did the inequality feel insecure?
Because it was never sure if it was greater than or less than — always comparing itself to others!
😲 Whoa!
GPS solves a system of equations from multiple satellites at once to find the single point where all their distances agree — your location.
✅ Quick check: Two lines cross at exactly one point. How many solutions does that system have?
Say your answer out loud first — then reveal.
One — the single (x, y) point where both equations are true.
The intersection is the only pair that satisfies both equations.
🧪 Try it! (2 minutes)
Graph y = x and y = 4 − x on paper. Where they cross is the solution to the system.