5
algebraHow many solutions does this system have?
A
No solution
B
Exactly one solution
C
Infinitely many solutions
D
Cannot be determined
Correct Answer: C
Choice C is the correct answer. Let's check if one equation is a multiple of the other.
Step 1: Divide the first equation by 5:
This is exactly the second equation!
Conclusion: Infinitely many solutions (identical lines)
💡 Strategic Tip: Always look for common factors in all terms—factoring simplifies comparison.
Choice A is incorrect because no solution requires parallel lines with different constants.
Choice B is incorrect because one solution requires different slopes.
Choice D is incorrect because simplification always reveals the relationship.