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When solving linear equations, one of the first steps is to isolate the variable. This means getting the variable by itself on one side of the equation.
In this exercise, we have the equation \[-8 + y = -23\].
To isolate the variable (in this case, \( y \)), we need to get rid of the \( -8 \) on the left side.

We can do this by adding \( 8 \) to both sides of the equation. This step is based on the addition principle, which states that whatever you add to one side of an equation, you must also add to the other side to keep it balanced.
So, adding \( 8 \) to both sides looks like this:
\[-8 + y + 8 = -23 + 8\]
Now we have successfully moved the \( 8 \) over, making it easier to solve for \( y \).

After isolating the variable, the next step is to simplify the equation.
This means performing any arithmetic operations needed to make the equation cleaner and more straightforward.
In our exercise's example, we have the equation from the previous step: \( -8 + y + 8 = -23 + 8 \).
When we simplify both sides, we perform the addition:
\[-8 + 8 + y = -15\]
Since \( -8 + 8 \) cancels out, we get:
\ y = -15 \
Simplifying equations can help you see the value of the variable more clearly. It minimizes the chances of making mistakes in calculation and solving. Remember, every equation may not be as simple as this one, but the process of simplifying remains the same: perform arithmetic operations according to mathematical rules to reduce the equation to its simplest form.

Solving linear equations generally involves getting the variable isolated and then simplifying the equation.
Here is a summary of the steps we followed in this exercise:

• First, we isolated the variable \( y \) by adding \( 8 \) to both sides.
• Next, we simplified the equation to find the value of \( y \).

The steps we discussed are foundational to solving any linear equation you might encounter.
Remember to always:

• Combine like terms.
• Perform inverse operations to isolate the variable.
• Simplify your equations step by step.

By understanding these core concepts, you'll be well-equipped to tackle more complex equations and enhance your problem-solving skills. Linear equations pop up everywhere in math, so mastering these steps is crucial!