- Start with the equation \(-8 = y + 9\).
- Subtract 9 from both sides to isolate the variable \(y\).
- Calculate \(-8 - 9 = -17\).
- The solution is \(\boxed{-17}\).
Explanation
- Problem Analysis
We are given a simple linear equation: \(-8 = y + 9\). Our objective is to find the value of the variable \(y\). To solve for \(y\), we need to isolate it on one side of the equation. This can be done by performing the same operation on both sides to keep the equality intact.
- Solving for y
To isolate \(y\), we subtract 9 from both sides of the equation:
\[-8 - 9 = y + 9 - 9\]
This simplifies the right side to just \(y\), while the left side becomes:
\[-8 - 9 = -17\]
Therefore, we have \(y = -17\).
Examples
Linear equations appear in everyday situations where you need to track changes or find an unknown starting point. For example, if you have a temperature sensor reading \(-8^\circ C\) and you know that the temperature just dropped by \(9^\circ C\) from a starting value \(y\), you can use the equation \(y - 9 = -8\) to find that the initial temperature was \(1^\circ C\). Similarly, this type of calculation is essential in accounting, physics, and basic engineering whenever you work with balanced equations.