Answer:
-6
Step-by-step explanation:
Let the first, second and third number be x, y and z respectively.
We are told that the second number is subtracted from the sum of the first number and 3 times the third number, the result is 2.
Thus;
(x + 3z) - y = 2 - - - (eq 1)
The third number plus 3 times the first number is -1.
Thus;
z + 3x = -1 - - - (eq 2)
The first number plus 3 times the second number plus the third number is -16.
Thus;
x + 3y + z = -16 - - - (eq 3)
From eq 2, we can rearrange to get;
z = -1 - 3x
Putting -1 - 3x for z in eq(1) and (eq 3),we have;
(x + 3(-1 - 3x)) - y = 2
x -3 - 9x - y = 2
-8x - y = 2 + 3
-8x - y = 5
y = -5 - 8x
Putting y = -5 - 8x and z = -1 - 3x into eq(3), we have;
x + 3(-5 - 8x) + (-1 - 3x) = -16
x - 15 - 24x - 1 - 3x = -16
-26x - 16 = -16
-26x = 16 + 16
x = 0
Since y = -5 - 8x, then y = -5 - 8(0)
y = - 5
Also, since z = -1 - 3x, then;
z = -1 - 3(0)
z = -1
The sum of the three numbers are;
x + y + z = 0 + (-5) + (-1) = -6
