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How many ordered pairs $(x, y)$ satisfy BOTH conditions below? 

$\bullet$  Condition I: $x = 1$ or $y = 0$ or $y = 2$ or $x = 0$ or $x = -1$

$\bullet$  Condition II: $x = 0$ or $x = 2$ or $y = 1$ or $y = 0$ or $y = -1$

 Aug 16, 2023
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To find the ordered pairs \((x, y)\) that satisfy both conditions, we need to identify the values that satisfy both Condition I and Condition II.

For Condition I, the possible pairs are:

1. \(x = 1\) and \(y\) can be any value.
2. \(y = 0\) and \(x\) can be any value.
3. \(y = 1\) and \(x\) can be any value.
4. \(x = 0\) and \(y\) can be any value.
5. \(x = -1\) and \(y\) can be any value.

For Condition II, the possible pairs are:

1. \(x = 0\) and \(y\) can be any value.
2. \(x = 2\) and \(y\) can be any value.
3. \(y = 1\) and \(x\) can be any value.
4. \(y = 0\) and \(x\) can be any value.
5. \(y = -1\) and \(x\) can be any value.

To satisfy both conditions, the ordered pairs must match the common values in both lists. The common values are \(x = 0\) and \(y = 0\) or \(y = 1\).

Therefore, the ordered pairs that satisfy both conditions are \((0, 0)\) and \((0,1)\), and there are \(\boxed{2}\) such pairs.

 Aug 16, 2023

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