Formulating a system of equations, we have:
x+y=-6 Equation 1
x-y=12 Equation 2
Solving the system of equations, we have:
y = -6 - x (Subtracting x from both sides of the Equation 1)
x - (-6 - x)=12 (Replacing y=-6-x in the Equation 2)
x + 6 + x = 12 (Using the sign rules)
2x + 6 = 12 (Adding like terms)
2x = 6 (Subtracting 6 from both sides of the Equation)
x=3 (Dividing on both sides by 2)
Replacing x=3 in y=-6-x , we have:
y = -6 - 3
y= -9
Given that the numbers are 3 and -9, the smallest of them is -9.
The answer is -9.
