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 = 345
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 = 219
Therefore, the two Numbers are 345 and 219
Check Sum of the two Numbers:
345 + 219 = 564 ✓
Check Difference between the two Numbers:
345 − 219 = 126 ✓
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 =
564 + 126/2
x =
690/2
x = 345
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 =
564 − 126/2
y =
438/2
y = 219
Therefore, the two Numbers are 345 and 219
Check Sum of the two Numbers:
| 1 | |||
| 3 | 4 | 5 | |
| 2 | 1 | 9 | |
| 5 | 6 | 4 |
Check Difference between the two Numbers:
| 3 | 15 | ||
| 3 | 4 | 5 | |
| − | 2 | 1 | 9 |
| 1 | 2 | 6 |
