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 = 821
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 = 763
Therefore, the two Numbers are 821 and 763
Check Sum of the two Numbers:
821 + 763 = 1,584 ✓
Check Difference between the two Numbers:
821 − 763 = 58 ✓
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 =
1,584 + 58/2
x =
1,642/2
x = 821
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 =
1,584 − 58/2
y =
1,526/2
y = 763
Therefore, the two Numbers are 821 and 763
Check Sum of the two Numbers:
| 1 | ||||
| 8 | 2 | 1 | ||
| 7 | 6 | 3 | ||
| 1 | 5 | 8 | 4 |
Check Difference between the two Numbers:
| 11 | |||
| 7 | 1 | 11 | |
| 8 | 2 | 1 | |
| − | 7 | 6 | 3 |
| 5 | 8 |
