m + n = -17
n = m - 5
Step-by-step explanation:
let the two numbers be m and n respectively
The sum of the two numbers = negative seventeen
The sum of the two numbers = -17
The sum of the two numbers = m + n
equating both:
m + n = -17 ...equation 1
One number is five less than the other:
let the first number = m
let the 2nd number = n
The 2nd number will be 5 less than the first
2nd number = m - 5
n = m - 5 ...equation 2
substituting for n in equation 1:
m + m - 5 = -17
2m - 5 = -17
add 5 to both sides:
2m - 5 + 5 = -17 + 5
2m = -12
divide both sides by 2:
2m/2 = -12/2
m = -6
substitute from m in equation 1:
-6 + n = - 17
add 6 to both sides:
-6 + 6 + n = -17 + 6
n = -11
The system of equations are:
m + n = -17 ...equation 1
n = m - 5 ...equation 2