Question

The sum of two numbers is negative twenty, and one number is six less than the other. Using the variables m and n to represent the two numbers, write a system of equations that describe the situation. Enter the equations below, separated by a comma. Next find the two numbers. Enter them below, separated by a comma.

Answer 1

`-13\text{ and -7}`

Step-by-step explanation:

Here, we want to get the values of the two numbers

We already have variables assigned to the the numbers

The sum of the two numbers is -20

We have this as:

`\text{m + n = -20}`

One of the numbers is six less than the other

We have this as:

`n\text{ = m + 6}`

We proceed to solve the two equations simultaneously

We start by susbtituting the second into the first:

`\begin{gathered} \text{ m + m + 6 = -20} \\ 2m\text{ + 6= -20} \\ 2m\text{ = -20-6} \\ 2m\text{ = -26} \\ m\text{ = -}(26)/(2) \\ m\text{ = -13} \end{gathered}`

To get n, we simply susbtitute into the equation for n above

We have this as:

`\begin{gathered} n\text{ = -13 + 6} \\ n\text{ = -7} \end{gathered}`