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In the xy-plane, if the solutions to the system of inequalities y < ax+1 and y > bx+1 are only in Quadrant I, which of the following relationships between a and b must be true? Choose 1 answer: (A) 0 > a > b (B) b > 0 > a (c) a > b > 0 (D) a > 0 > b

In the xy x y -plane, if the solutions to the system of inequalities y⟨ax+1 y\langle a x+1 and y⟩bx+1 y\rangle b x+1 are only in Quadrant I, which of the following relationships between a a and b b must be true?\newlineChoose 11 answer:\newline(A) 0>a>b \newline(B) b>0>a \newline(C) a>b>0 \newline(D) a>0>b

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Q. In the xy x y -plane, if the solutions to the system of inequalities y⟨ax+1 y\langle a x+1 and y⟩bx+1 y\rangle b x+1 are only in Quadrant I, which of the following relationships between a a and b b must be true?\newlineChoose 11 answer:\newline(A) 0>a>b 0>a>b \newline(B) b>0>a b>0>a \newline(C) a>b>0 a>b>0 \newline(D) a>0>b a>0>b
  1. Identify Quadrant I: Identify the characteristics of Quadrant I: In Quadrant I, both xx and yy are positive. This means for the inequalities y < ax+1 and y > bx+1 to have solutions only in this quadrant, both expressions ax+1ax+1 and bx+1bx+1 must yield positive values when xx is positive.
  2. Analyze y < ax+1: Analyze the inequality y < ax+1: For y < ax+1 to be true in Quadrant I, the slope aa must be positive. This ensures that as xx increases, ax+1ax+1 also increases, keeping yy positive and below the line ax+1ax+1.
  3. Analyze y > bx+1: Analyze the inequality y > bx+1: For y > bx+1 to be true in Quadrant I, the slope bb must also be positive. However, since yy is also less than ax+1ax+1, the line bx+1bx+1 must be below ax+1ax+1 for all positive xx. This implies that bb must be less than y > bx+100.
  4. Combine Findings: Combine the findings: From the analysis, we have determined that both aa and bb must be positive, and bb must be less than aa. This corresponds to the condition a > b > 0.

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