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 = 25
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 = 16
Therefore, the two Numbers are 25 and 16
Check Sum of the two Numbers:
25 + 16 = 41 ✓
Check Difference between the two Numbers:
25 − 16 = 9 ✓
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 =
41 + 9/2
x =
50/2
x = 25
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 =
41 − 9/2
y =
32/2
y = 16
Therefore, the two Numbers are 25 and 16
Check Sum of the two Numbers:
| 1 | ||
| 2 | 5 | |
| 1 | 6 | |
| 4 | 1 |
Check Difference between the two Numbers:
| 1 | 15 | |
| 2 | 5 | |
| − | 1 | 6 |
| 9 |
