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 = 834
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 = 799
Therefore, the two Numbers are 834 and 799
Check Sum of the two Numbers:
834 + 799 = 1,633 ✓
Check Difference between the two Numbers:
834 − 799 = 35 ✓
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 =
1,633 + 35/2
x =
1,668/2
x = 834
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 =
1,633 − 35/2
y =
1,598/2
y = 799
Therefore, the two Numbers are 834 and 799
Check Sum of the two Numbers:
| 1 | 1 | 1 | ||
| 8 | 3 | 4 | ||
| 7 | 9 | 9 | ||
| 1 | 6 | 3 | 3 |
Check Difference between the two Numbers:
| 12 | |||
| 7 | 2 | 14 | |
| 8 | 3 | 4 | |
| − | 7 | 9 | 9 |
| 3 | 5 |
