Let's solve the equation \( y^2 + 4x - 14y = -53 \).

We are trying to simplify or solve for one of the variables. However, since this is a multivariable equation, it is possible to isolate one variable in terms of the other. Let's express \( x \) in terms of \( y \).

### Steps:
1. **Rearrange the equation:**
   \[
   y^2 - 14y + 4x = -53
   \]
2. **Isolate \( 4x \):**
   \[
   4x = -53 - y^2 + 14y
   \]
3. **Solve for \( x \):**
   \[
   x = \frac{-53 - y^2 + 14y}{4}
   \]

Thus, the solution in terms of \( x \) is:
\[
x = \frac{-53 - y^2 + 14y}{4}
\]

Would you like to go over the steps or explore a different approach?

### Related Questions:
1. How would the equation change if we were solving for \( y \) in terms of \( x \)?
2. What happens if we try completing the square on the \( y^2 - 14y \) part?
3. How does changing the constant value on the right-hand side affect the result?
4. How can we interpret this equation geometrically?
5. What if the equation were \( y^2 + 4x - 14y = 0 \)? How would that affect the solution?

### Tip:
When dealing with equations involving multiple variables, isolating one variable can make solving easier and help understand relationships between variables.

Explore how to solve the multivariable equation y² + 4x - 14y = -53 by isolating one variable. Learn the step-by-step process of rearranging and simplifying equations, focusing on algebraic techniques and relationships between variables. Suitable for Grades 9-11.

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