{[y = -(1)/(3)x+3],[y (3)/(4)x-1]:} Which quadrants contain the solution to this system of inequalities? A. quadrants I, II, and IV B. quadrants I and II C. quadrants II and III D. quadrants I and IV

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{[y >= -(1)/(3)x+3],[y > (3)/(4)x-1]:} Which quadrants contain the solution to this system of inequalities? A. quadrants I, II, and IV B. quadrants I and II C. quadrants II and III D. quadrants I and IV

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Analyze Line Inequality: Analyze the first inequality [y >= -(1)/(3)x+3]. This inequality represents a line with a negative slope that crosses the y-axis at (0, 3). Since y is greater than or equal to this line, the solution set is above the line. This line divides the coordinate plane into two regions: above the line (where the inequality holds) and below the line (where the inequality does not hold).Analyze Positive Slope: Analyze the second inequality [y > (3)/(4)x-1]. This inequality represents a line with a positive slope that crosses the y-axis at (0, -1). Since y is greater than this line, the solution set is above the line. This line also divides the coordinate plane into two regions: above the line (where the inequality holds) and below the line (where the inequality does not hold).Determine Common Quadrants: Determine the quadrants where both inequalities are satisfied. The first inequality's solution set is above the line with a negative slope, which includes parts of quadrants I, II, and III. The second inequality's solution set is above the line with a positive slope, which includes parts of quadrants I and II. The common regions where both inequalities are satisfied are in quadrants I and II.Confirm Excluded Quadrants: Confirm that no other quadrants are included in the solution set. Quadrant III is not included because the first inequality requires y to be above the line with a negative slope, which does not occur in quadrant III. Quadrant IV is not included because the second inequality requires y to be above the line with a positive slope, which does not occur in quadrant IV.

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