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The system a1 x + b1 y = c1 and a2 x + b2 y = c2 (with all of a1,b1,c1,a2,b2,c2 nonzero) has infinitely many solutions. Then:

1. a1/a2 = b1/b2 = c1/c2
2. (a1 + a2)/(a1 - a2) = (b1 + b2)/(b1 - b2) = (c1 + c2)/(c1 - c2)
3. the quadratics a1 x² + b1 x + c1 = 0 and a2 x² + b2 x + c2 = 0 have no common root
4. the system a1² x + b1² y = c1² c2 and a1² x + b1² y = c1 c2² also has infinitely many solutions

Correct answer: a1/a2 = b1/b2 = c1/c2

Solution

Two linear equations have infinitely many solutions iff a1/a2 = b1/b2 = c1/c2.

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