Final answer:
To solve this problem, assume that the first number is x and the second number is y. Set up the equations 4x - 2y = -16 and x + y = -1. Solve the system of equations using the elimination method to find the values of x and y. The two numbers are -3 and 2.
Step-by-step explanation:
To solve this problem, let's use algebra. Let's assume that the first number is x and the second number is y. According to the problem, 4 times a number minus twice another number is -16, so we can set up the equation 4x - 2y = -16.
We are also given that the sum of the two numbers is -1, so we can set up the equation x + y = -1.
To solve this system of equations, we can use either the substitution or elimination method. Let's use the elimination method. Multiply the second equation by 2 to make the coefficients of y the same in both equations.
The equations become:
4x - 2y = -16
2x + 2y = -2
Add the two equations together, eliminating y:
6x = -18
Divide both sides by 6 to solve for x:
x = -3
Substitute this value of x back into one of the original equations to solve for y. Let's use the second equation:
-3 + y = -1
Add 3 to both sides:
y = 2
Therefore, the two numbers are -3 and 2.