9
algebra

Determine the number of solutions: {7x14y=21x2y=3\begin{cases} 7x - 14y = 21 \\ x - 2y = 3 \end{cases}

A

No solution

B

Exactly one solution

C

Infinitely many solutions

D

Exactly three solutions

Correct Answer: C

Choice C is the correct answer. Let's simplify the first equation.

Step 1: Divide the first equation by 7: 7x14y7=217\frac{7x - 14y}{7} = \frac{21}{7}x2y=3x - 2y = 3

This is exactly the second equation!

Step 2: Both equations represent the same line, 💡 Strategic Tip: Always simplify equations by factoring out common factors before comparing.

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 linear equations cannot have exactly three solutions.