What are the ordered pairs that represent solutions to the equation x * y = 2?

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.

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