1. **State the problem:** We need to solve for variables $b$, $A$, and $C$ given an equation or system involving these variables. Since no specific equation is provided, let's consider a general approach. 2. **General approach:** To solve for variables, you need as many independent equations as variables. For example, if you have three variables $b$, $A$, and $C$, you need three independent equations. 3. **Example system:** Suppose we have the system: $$ \begin{cases} A + b = 10 \\ 2A - C = 3 \\ b + C = 7 \end{cases} $$ 4. **Step-by-step solution:** - From the first equation: $b = 10 - A$ - Substitute $b$ into the third equation: $(10 - A) + C = 7 \Rightarrow C = 7 - 10 + A = A - 3$ - Substitute $C$ into the second equation: $2A - (A - 3) = 3 \Rightarrow 2A - A + 3 = 3 \Rightarrow A + 3 = 3 \Rightarrow A = 0$ - Then $b = 10 - 0 = 10$ - And $C = 0 - 3 = -3$ 5. **Final answer:** $$ A = 0, \quad b = 10, \quad C = -3 $$ This method applies generally: write down your equations, isolate variables, substitute, and solve step-by-step.