It is known that a, B and C are all nonnegative numbers and satisfy the equations 3A + 2B + C = 5 and 2A + b-3c = 1. If M = 3A + b-7c, the maximum and minimum values of M are obtained Tip: apply inequality knowledge.

Detailed answers are as follows:
The first step is to find the unary expression of M = 3A + b-7c
Solving equations
3a+2b+c=5.（1）
2a+b-3c=1.（2）
have to
a-7c=-3.(3)
b+11c=7.(4)
From (1) - (4), it is obtained that:
3A + b-10c = - 2, that is 3A + b-7c = 3c-2
So: M = 3A + b-7c = 3c-2. (5)
Step 2: find out the value range of C
Because a, B and C are all nonnegative numbers, so
From (3): a = 7c-3 ≥ 0
c≥3/7
From (4): B = 7-11c ≥ 0
c≤7/11
So 3 / 7 ≤ C ≤ 7 / 11 ≤ 7 / 11
Step 3: Discussion
① When C = 7 / 11, substituting (5) m, the maximum value is - 1 / 11
② When C = 3 / 7, substituting (5) m is the smallest, which is - 5 / 7

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