5
algebra

How many solutions does this system have? {15x20y=253x4y=5\begin{cases} 15x - 20y = 25 \\ 3x - 4y = 5 \end{cases}

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: 15x20y5=255\frac{15x - 20y}{5} = \frac{25}{5}3x4y=53x - 4y = 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.