Set 12: Linear Inequalities

Explanation

Answer: A

Find the coordinates of the vertex formed by $y = 2x$ and $x + y = 6$ .

$(2, 4)$

✓ Correct

$(3, 3)$

$(1, 5)$

$(4, 2)$

Detailed Explanation

Choice A is correct. Choice A is the correct answer. Solve the system of equations. 1. Substitute: $y = 2 x$ into $x + y = 6$ 2. Solve: $x + (2 x) = 6 \rightarrow 3 x = 6 \rightarrow x = 2$ 3. Find y: $y = 2(2) = 4$ 4. Vertex: $(2, 4)$ Strategic Tip: Vertices of feasible regions are found by treating inequalities as equations. Choice B is incorrect. Choice C is incorrect. Choice D is incorrect.

Key Steps:

•

The correct answer is $(2, 4)$

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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