Let's analyze the problem shown in the image.

The given information is:

(b) If $(x - 1, 11) = (8, y + 3)$, then $\sqrt{x + 2y} = \ldots$

Step 1: Solving for $x$ and $y$

Given that two ordered pairs are equal:

$(x - 1, 11) = (8, y + 3)$

This implies that:

1. $x - 1 = 8$
2. $11 = y + 3$

Solving the equations:

1. $x - 1 = 8 \Rightarrow x = 8 + 1 = 9$
2. $11 = y + 3 \Rightarrow y = 11 - 3 = 8$

So, $x = 9$ and $y = 8$.

Step 2: Finding $\sqrt{x + 2y}$

Now, substitute $x = 9$ and $y = 8$ into the expression $\sqrt{x + 2y}$:

$\sqrt{x + 2y} = \sqrt{9 + 2(8)} = \sqrt{9 + 16} = \sqrt{25} = 5$

Final Answer

$\sqrt{x + 2y} = 5$

Let me know if you would like a detailed explanation of any step, or if you have more questions.

Additional Related Questions:

1. What would happen if $x$ and $y$ were variables instead of specific values?
2. How would the value of $\sqrt{x + 2y}$ change if $x$ was increased by 2?
3. How would you solve the problem if $x$ and $y$ were complex numbers?
4. What is the geometric interpretation of the given pair equality?
5. How would you find $\sqrt{x + 2y}$ if it involved additional constraints?

Tip

Always make sure to isolate variables systematically when dealing with equal pairs to avoid confusion.