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 = 987
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 = 109
Therefore, the two Numbers are 987 and 109
Check Sum of the two Numbers:
987 + 109 = 1,096 ✓
Check Difference between the two Numbers:
987 − 109 = 878 ✓
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 =
1,096 + 878/2
x =
1,974/2
x = 987
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 =
1,096 − 878/2
y =
218/2
y = 109
Therefore, the two Numbers are 987 and 109
Check Sum of the two Numbers:
| 1 | 1 | |||
| 9 | 8 | 7 | ||
| 1 | 0 | 9 | ||
| 1 | 0 | 9 | 6 |
Check Difference between the two Numbers:
| 7 | 17 | ||
| 9 | 8 | 7 | |
| − | 1 | 0 | 9 |
| 8 | 7 | 8 |
