To find the ordered pairs that satisfy the equation x * y = 2, we can start by rearranging this relationship into a form that will allow us to generate pairs of solutions easily.
First, we can express y in terms of x:
y = 2 / x
Now, let’s explore some specific values for x to find the corresponding y values:
- If x = 1, then y = 2 / 1 = 2. Thus, the ordered pair is (1, 2).
- If x = 2, then y = 2 / 2 = 1. Thus, the ordered pair is (2, 1).
- If x = -1, then y = 2 / -1 = -2. Thus, the ordered pair is (-1, -2).
- If x = -2, then y = 2 / -2 = -1. Thus, the ordered pair is (-2, -1).
- If x = 0.5, then y = 2 / 0.5 = 4. Thus, the ordered pair is (0.5, 4).
- If x = 4, then y = 2 / 4 = 0.5. Thus, the ordered pair is (4, 0.5).
- If x = -0.5, then y = 2 / -0.5 = -4. Thus, the ordered pair is (-0.5, -4).
- If x = -4, then y = 2 / -4 = -0.5. Thus, the ordered pair is (-4, -0.5).
From these examples, we can compile a list of ordered pairs that are solutions to the equation:
- (1, 2)
- (2, 1)
- (-1, -2)
- (-2, -1)
- (0.5, 4)
- (4, 0.5)
- (-0.5, -4)
- (-4, -0.5)
These pairs can help visualize how the product of x and y equals 2 across different points in the Cartesian plane.