9

Set 1: Linear Functions (Intermediate)

Explanation

Answer: A

How many solutions does the system 2x+y=52x + y = 5 and 4x+2y=104x + 2y = 10 have?

A.

Infinitely many

✓ Correct
B.

No solution

C.

Exactly one

D.

Two

Detailed Explanation

Choice A is correct. Choice A is the correct answer. Check for coincident lines. 1. Equation 2: Divide by 2 2x+y=5\rightarrow 2 x + y = 5. 2. Comparison: It is identical to Equation 1. 3. Result: Same line \rightarrow Infinite solutions. Strategic Tip: If one equation is a multiple of the other, they are the same line. Choice B is incorrect because they touch everywhere. Choice C is incorrect because they are not distinct. Choice D is incorrect because linear systems never have exactly two solutions.

Key Steps:

The correct answer is Infinitely many

Why others are wrong:
B: Choice B is incorrect and may result from a calculation error.
C: Choice C is incorrect and may result from a calculation error.
D: Choice D is incorrect and may result from a calculation error.

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