3
algebra

Determine the number of solutions: {y=4x78x2y=14\begin{cases} y = 4x - 7 \\ 8x - 2y = 14 \end{cases}

A

Infinitely many solutions

B

No solution

C

Exactly one solution

D

Exactly two solutions

Correct Answer: A

Choice A is the correct answer. Let's rearrange the first equation to compare with the second.

Step 1: Rearrange y=4x7y = 4x - 7 to standard form: 4x+y=7-4x + y = -7 Multiply by -2: 8x2y=148x - 2y = 14

This is exactly the second equation!

Step 2: Since both equations represent the same line, there are infinitely many solutions.

💡 Strategic Tip: Always convert to the same form (slope-intercept or standard) to compare equations easily.

Choice B is incorrect because no solution requires parallel lines that don't overlap.

Choice C is incorrect because one solution requires different slopes.

Choice D is incorrect because two linear equations cannot have exactly two solutions.