The following is known about three numbers: If the second number is subtracted from the sum of the first number and 3 times the third number, the result is 2. The third number plus 3 times the first number is -1. The first number plus 3 times the second number plus the third number is -16. Find the sum of the three numbers.

-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

5

step-by-step explanation: