Let's solve the equation step by step:

### Given equation:
\[
3x + 27 + x - 45 = 2x - 8 + y
\]

### Step 1: Combine like terms on both sides
On the left-hand side, combine the terms with \(x\) and the constant terms:
\[
(3x + x) + (27 - 45) = 2x - 8 + y
\]
This simplifies to:
\[
4x - 18 = 2x - 8 + y
\]

### Step 2: Move all \(x\)-terms to one side
Subtract \(2x\) from both sides to move the terms involving \(x\) to the left:
\[
(4x - 2x) - 18 = -8 + y
\]
This simplifies to:
\[
2x - 18 = -8 + y
\]

### Step 3: Solve for \(y\)
Add 18 to both sides to isolate \(2x\) on the left:
\[
2x = -8 + 18 + y
\]
Simplify the constants:
\[
2x = 10 + y
\]

Finally, solve for \(y\):
\[
y = 2x - 10
\]

### Final Answer:
\[
y = 2x - 10
\]

Would you like a detailed explanation of any specific step or have questions about this process?

Here are some related questions you might find helpful:
1. How would the solution change if the constant term were different?
2. What happens if the equation involves more variables?
3. How can we graph the equation \(y = 2x - 10\)?
4. What is the slope and intercept of \(y = 2x - 10\)?
5. How do you solve for \(x\) in similar equations?

**Tip:** When combining like terms, ensure you handle constants and variable terms separately to avoid confusion!

Learn how to solve the linear equation 3x + 27 + x - 45 = 2x - 8 + y with a step-by-step solution. This problem covers core algebraic concepts such as combining like terms and solving for variables. Suitable for students in Grades 8-10.

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