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 = 505,000
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 = 495,000
Therefore, the two Numbers are 505,000 and 495,000
Check Sum of the two Numbers:
505,000 + 495,000 = 1,000,000 ✓
Check Difference between the two Numbers:
505,000 − 495,000 = 10,000 ✓
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 =
1,000,000 + 10,000/2
x =
1,010,000/2
x = 505,000
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 =
1,000,000 − 10,000/2
y =
990,000/2
y = 495,000
Therefore, the two Numbers are 505,000 and 495,000
Check Sum of the two Numbers:
| 1 | 1 | 1 | |||||
| 5 | 0 | 5 | 0 | 0 | 0 | ||
| 4 | 9 | 5 | 0 | 0 | 0 | ||
| 1 | 0 | 0 | 0 | 0 | 0 | 0 |
Check Difference between the two Numbers:
| 4 | 10 | |||||
| 5 | 0 | 5 | 0 | 0 | 0 | |
| − | 4 | 9 | 5 | 0 | 0 | 0 |
| 1 | 0 | 0 | 0 | 0 |
