The given equation is:

\[
x = \pm \sqrt{1 - y}
\]

This represents a relationship between \( x \) and \( y \), where the value of \( x \) depends on \( y \), and you take both the positive and negative square roots.

### Key steps to interpret this equation:

1. **Square Root Component**: \( \sqrt{1 - y} \) means that the expression inside the square root, \( 1 - y \), must be non-negative (i.e., \( 1 - y \geq 0 \)), otherwise, the result would be complex.
   
   \[
   1 - y \geq 0 \quad \Rightarrow \quad y \leq 1
   \]

2. **Positive and Negative Solutions**: The \( \pm \) sign indicates that there are two possible values for \( x \): one where \( x \) is the positive square root of \( 1 - y \), and the other where \( x \) is the negative square root.

Thus, the equation can be rewritten as:
\[
x = +\sqrt{1 - y} \quad \text{or} \quad x = -\sqrt{1 - y}
\]

The domain of this function is restricted to \( y \leq 1 \) to ensure that the square root remains real.

Would you like me to further expand on this topic or explore any specific applications or transformations of the equation?

### 5 Related Questions:
1. How would you solve for \( y \) in terms of \( x \) from the given equation?
2. What is the domain and range of this equation?
3. Can you graph the function \( x = \pm \sqrt{1 - y} \)?
4. How would this equation change if the \( \pm \) sign was removed?
5. How do you handle the case when \( y > 1 \) in similar equations?

### Tip:
When dealing with square roots in equations, always ensure that the expression under the root is non-negative to avoid complex solutions.

Explore how to solve the equation x = ±√(1 - y) with detailed explanations on square roots, domain restrictions, and the effect of positive and negative solutions. Ideal for students in Grades 9-11 learning algebra and functions.

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