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 = 23
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 = 14
Therefore, the two Numbers are 23 and 14
Check Sum of the two Numbers:
23 + 14 = 37 ✓
Check Difference between the two Numbers:
23 − 14 = 9 ✓
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 =
37 + 9/2
x =
46/2
x = 23
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 =
37 − 9/2
y =
28/2
y = 14
Therefore, the two Numbers are 23 and 14
Check Sum of the two Numbers:
| 2 | 3 | |
| 1 | 4 | |
| 3 | 7 |
Check Difference between the two Numbers:
| 1 | 13 | |
| 2 | 3 | |
| − | 1 | 4 |
| 9 |
