Problem 75 - College Algebra

Question

List the quadrant or quadrants satisfying each condition. $$x y>0$$

Step-by-Step Solution

Answer

The condition, x*y > 0 is satisfied in Quadrant I and Quadrant III of the Cartesian Plane.

Step 1: Understanding the Cartesian Plane

The Cartesian Plane comprises four quadrants: Quadrant I where x>0 and y>0; Quadrant II where x<0 and y>0; Quadrant III where x<0 and y<0; and Quadrant IV where x>0 and y<0. The condition xy > 0 signifies that x and y are of the same sign.

Step 2: Identifying the Quadrants

We need to identify the quadrants where both x and y are either positive or negative. In the first quadrant (Quadrant I), both x and y are positive. So, their product will be positive. In the third quadrant (Quadrant III), both x and y are negative. But the product of two negative numbers is also positive. Therefore, x*y will be positive in both these quadrants.