Answer:
The numbers are 3, 5, -10.
Step-by-step explanation:
Let, the numbers are X, Y, Z.
Given, sum of the three numbers are -2.
So, the equation is X + Y+ Z = -2 .......(i)
Again, for 2nd condition, the equation will be
3X + 2Y + Z = 9 ....... (ii)
Again, for the third condition, the equation will be
Y - (Z/2) = 10 ......(iii)
Multiplying the equation (i) by 3 and the equation (ii) by 1, we get
3X + 3Y+ 3Z = -6
<u> 3X + 2Y + Z = 9</u>
(Deduct) Y + 2Z = -15 ......(iv)
Solving equation (iii) and (iv) we get,
Y - (Z/2) = 10
<u> Y + 2Z = -15</u>
(Deduct) -(Z/2) - 2Z = 25
or, (-Z-4Z)/2 = 25
or, -5Z = 25*2
or, Z = 50/(-5)
Therefore, Z = -10
Putting the value of Z into equation (iv) we get,
Y + 2*(-10) = -15
or, Y - 20 = -15
or, Y = 20 - 15
Therefore, Y = 5
Putting the value of Y and Z into equation (i) we get,
X + 5 + (-10) = -2
or, X + 5 - 10 = -2
or, X - 5 = -2
or, X = 5 - 2
Therefore, X = 3
So, the numbers are, X = 3; Y = 5; and Z = -10.
