Set 1: Linear Functions (Intermediate)

Explanation

Answer: A

For what value of $k$ will the system $3x - y = 4$ and $6x - ky = 8$ have infinitely many solutions?

$2$

✓ Correct

$-2$

$1$

$6$

Detailed Explanation

Choice A is correct. Choice A is the correct answer. Coincident lines. 1. Compare: Equation 2 should be a multiple of Equation 1. 2. Ratio: $6x / 3 x = 2$ . The multiplier is 2. 3. Apply: Multiply the y-term of Eq 1 by 2: $(-1) \times 2 = -2$ . 4. Match: The y-term in Eq 2 is $-k$ . So $-k = -2 \rightarrow k = 2$ . Strategic Tip: For infinite solutions, $A_1/A_2 = B_1/B_2 = C_1/C_2$ . Choice B is incorrect because sign error. Choice C is incorrect. Choice D is incorrect.

Key Steps:

•

The correct answer is $2$

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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