Interactive applet
Systems of Linear Equations
Two race cars run parallel lanes at speeds you set. One meeting, no meeting, or always the same mark — the three cases of a linear system.
Hands-on lab
Race · graph · three cases
Two race cars run two parallel lanes. A solution is a time when they are at the same mark — not the same lane. Position is linear in time: d = start + speed · t.
Teal car
d = 1 + 1.5t
Coral car
d = 7 + 0.5t
The system
d = 1 + 1.5t
d = 7 + 0.5t
One solution: t = 6 s, d = 10 m. That ordered pair is where both equations are true.
Missions
- Watch them meet once (one solution)
- Same speed, different starts (no solution)
- Same start and speed (infinitely many)
1/3 complete
Guided questions
Play the race. At what time are the cars at the same mark? What ordered pair is that on the graph?
Reflection
A solution of a system is a pair (t, d) that makes both equations true. Why is that the same as the cars being at the same mark at the same time?
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