Question

The sum of two numbers is negative fifteen, and one number is five less than the other. Using the variables m and n to represent the two numbers, write a system of equations that describe the solutions. Enter the equations below, separated by a comma.Find the two numbers. Enter them below, separated by a comma

Answer 1

We need to use the variables m and n to represent both numbers.

Their sum must equal -15. Therefore, we can write the next equation:

m + n = -15

If one number is five less than the other, we need to choose one variable and then we can write it in terms of the other variable. Then:

n = m-5

To find the value for each number, we can replace the n equation on the first equation:

m + n = -15

m + (m-5)= -15

Then:

m + m - 5 = -15

2m -5 = -15

Solve the equation for m:

Add both sides 5 units:

2m - 5 +5 = -15+5

2m = -10

Divide both sides by 2:

2m/2 = -10/2

m = -5

Finally, replace the m value on the first equation:

m + n = -15

-5 + n = -15

Then, solve the equation for n:

Add both sides by 5:

-5+5 + n = -15 +5

n = -10

Hence, both numbers are m=-5 and n= -10.

The equations separated by a comma are m + n = -15,n = m-5.

The numbers separated by a comma are -5,-10.