Linear Diophantine Puzzle III

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Each of the letters A, B, C, D, E stands for a different integer from 1 to 5 (so together they use each of 1, 2, 3, 4, 5 exactly once). The following equations hold:

D - 2 = C
E + C = D
A + E = C

Give the values of A, B, C, D, E in that order, separated by commas.

Each of the letters A, B, C, D, E stands for a different integer from 1 to 5 (so together they use each of 1, 2, 3, 4, 5 exactly once). The following equations hold:

D - 2 = C
E + C = D
A + E = C

Give the values of A, B, C, D, E in that order, separated by commas.