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 = 97
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 = 68
Therefore, the two Numbers are 97 and 68
Check Sum of the two Numbers:
97 + 68 = 165 ✓
Check Difference between the two Numbers:
97 − 68 = 29 ✓
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 =
165 + 29/2
x =
194/2
x = 97
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 =
165 − 29/2
y =
136/2
y = 68
Therefore, the two Numbers are 97 and 68
Check Sum of the two Numbers:
| 1 | 1 | ||
| 9 | 7 | ||
| 6 | 8 | ||
| 1 | 6 | 5 |
Check Difference between the two Numbers:
| 8 | 17 | |
| 9 | 7 | |
| − | 6 | 8 |
| 2 | 9 |
