To find the ordered pairs that solve the equation 2xy = 9, we first need to express one variable in terms of the other. Let’s solve for y.
Starting with the equation:
2xy = 9We can isolate y by dividing both sides by 2x (assuming x is not zero):
y = 9 / (2x)Now, we can generate ordered pairs by selecting different values for x and calculating the corresponding y values. Remember, it’s vital that x is not zero, as it would lead to division by zero.
Here are some example pairs:
- For x = 1: y = 9 / (2 * 1) = 4.5 → Ordered pair: (1, 4.5)
- For x = 2: y = 9 / (2 * 2) = 2.25 → Ordered pair: (2, 2.25)
- For x = 3: y = 9 / (2 * 3) = 1.5 → Ordered pair: (3, 1.5)
- For x = 4.5: y = 9 / (2 * 4.5) = 1 → Ordered pair: (4.5, 1)
- For x = 0.5: y = 9 / (2 * 0.5) = 9 → Ordered pair: (0.5, 9)
These ordered pairs are just a few examples. You can choose any non-zero value for x to find a corresponding value of y that satisfies the equation. Remember, the solution can be represented as:
(x, y) = (x, 9 / (2x))In summary, the pairs that solve the equation 2xy = 9 can be found by plugging in various values for x and calculating y accordingly.