What you’ll learn
Identify no/infinite solution systems.
Key idea
Equal slopes can describe either one common line or two distinct parallel lines.
Matching slopes alone cannot distinguish coincident from distinct parallel lines.
Worked example
Classify examples and non-examples for the concept 'Identify no/infinite solution systems'.
Classify the solution set of R: y=-3x+1; B: y=-3x+1. Choose with mathematical evidence.
Marked coordinates: C=(-2, 7); C=(-1, 4); C=(0, 1); C=(1, -2); C=(2, -5).
- Both slopes are -3; intercepts are 1 and 1.
- The equations are identical, so every point on their common line satisfies both.
Answer: infinitely many solutions — equal slopes and equal intercepts give one common line.
Quick Check
Classify examples and non-examples for the concept 'Identify no/infinite solution systems'.
Classify the solution set of R: y=-2x+0; B: y=-2x+2. Choose with mathematical evidence.
Marked coordinates: B=(-2, 6); R=(-2, 4); B=(-1, 4); R=(-1, 2); B=(0, 2); R=(0, 0); B=(1, 0); R=(1, -2); B=(2, -2); R=(2, -4).