To solve the problem of finding (a + b + c), let’s assume the following system of equations (a common problem fitting the description):

Problem Statement

Given the system of equations:
[ \begin{cases} a + 2b + 3c = 14 \ 2a + 3b + c = 11 \ 3a + b + 2c = 11 \end{cases} ]
Find the value of (a + b + c).

Step-by-Step Solution

Step 1: Add all three equations
Add the left-hand sides (LHS) and right-hand sides (RHS) of the equations together:
[ (a + 2b + 3c) + (2a + 3b + c) + (3a + b + 2c) = 14 + 11 + 11 ]

Step 2: Simplify both sides
Combine like terms on the LHS:
[ (a + 2a + 3a) + (2b + 3b + b) + (3c + c + 2c) = 36 ]
[ 6a + 6b + 6c = 36 ]

Step 3: Factor out 6 from the LHS
[ 6(a + b + c) = 36 ]

Step 4: Solve for (a + b + c)
Divide both sides by 6:
[ a + b + c = \frac{36}{6} = 6 ]

Answer: (\boxed{6})

作者声明:本文包含人工智能生成内容。