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Let the numbers be x and y:-

If: x+3y = -4 and 3x+y = 44

Then: 3x+9y = -12 and 3x+y = 44

Subtracting 3x+9y = -12 from 3x+y = 44: -8y = 56 => y = -7

By substitution: x = 17 and y = -7

Check: 17+3(-7) = -4

Check: 3(17) -7 = 44

Therefore the two numbers are: 17 and -7

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