Final answer:
To solve for y in the equation z = 5 - y, you add y to both sides then subtract z from both sides, resulting in y = 5 - z.
The final answer is \( y = -z + 5 \).
Step-by-step explanation:
To solve for y in the equation z = 5 - y,
Certainly! Let's go through the steps of solving the equation \( z = 5 - y \) for \( y \).
Starting with the original equation:
\[ z = 5 - y \]
**Subtract 5 from both sides:**
Subtracting 5 from both sides moves the constant term (5) to the other side of the equation.
\[ z - 5 = -y \]
. **Multiply both sides by -1:**
Multiplying both sides by -1 is done to isolate the variable term (-y) on one side.
\[ -1 \cdot (z - 5) = y \]
**Distribute -1 on the left side:**
\[ -z + 5 = y \]
Rearranging the terms, we get \( y = -z + 5 \).
So, the solution for \( y \) is \( y = -z + 5 \). This means that if you substitute this expression for \( y \) back into the original equation \( z = 5 - y \), the equation holds true.