Define variables:
Let x = larger number and y = smaller number
Resulting system of equations:
x + y = Sum
x − y = Difference
Solve the system of equations for x (larger number):
x =
Find x by substituting given Sum and Difference into equation for x and simplify:
x =
x =
x = 14.5
Solve the system of equations for y (smaller number):
y =
Find y by substituting given Sum and Difference into equation for y and simplify:
y =
y =
y = 6.5
Therefore, the two Numbers are 14.5 and 6.5
Check Sum of the two Numbers:
14.5 + 6.5 = 21 (trailing zero and decimal point are dropped) ✓
Check Difference between the two Numbers:
14.5 − 6.5 = 8 (trailing zero and decimal point are dropped) ✓
Let x = larger number and y = smaller number
Resulting system of equations:
x + y = Sum
x − y = Difference
Solve the system of equations for x (larger number):
x =
Sum + Difference/2
Find x by substituting given Sum and Difference into equation for x and simplify:
x =
21 + 8/2
x =
29/2
x = 14.5
Solve the system of equations for y (smaller number):
y =
Sum − Difference/2
Find y by substituting given Sum and Difference into equation for y and simplify:
y =
21 − 8/2
y =
13/2
y = 6.5
Therefore, the two Numbers are 14.5 and 6.5
Check Sum of the two Numbers:
| 1 | 1 | |||
| 1 | 4 | . | 5 | |
| 6 | . | 5 | ||
| 2 | 1 | . | 0 |
Check Difference between the two Numbers:
| 0 | 14 | |||
| 1 | 4 | . | 5 | |
| − | 6 | . | 5 | |
| 8 | . | 0 |
