Question

The sum of three numbers is 16. The sum of the first number and the second number is 2 more than the third number. The second number minus the sum of the first number and third number is twice the third number.

Answer 1

x = -6, y = 15 and z = 7.

Step-, by-step explanation:

x + y + z = 16

x + y = z + 2

y - (x + z) = 2z

Rearranging into the same form:

x + y + z = 16 A

x + y - z = 2 B

-x + y - 3z = 0 C

Subtracting A - B to eliminate x and y:

2z = 14

z = 7.

Substitute z = 7 in equations B and C:

x + y - 7 = 2

-x + y - 3(7) = 0

Adding these 2 equations to eliminate x:

2y - 28 = 2

2y = 30

y = 15.

Finally substitute for y and z in equation A to find x:

x + 7 + 15 = 16

x = 16 - 22

x = -6.