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 = 15
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 = 10
Therefore, the two Numbers are 15 and 10
Check Sum of the two Numbers:
15 + 10 = 25 ✓
Check Difference between the two Numbers:
15 − 10 = 5 ✓
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 =
25 + 5/2
x =
30/2
x = 15
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 =
25 − 5/2
y =
20/2
y = 10
Therefore, the two Numbers are 15 and 10
Check Sum of the two Numbers:
| 1 | 5 | |
| 1 | 0 | |
| 2 | 5 |
Check Difference between the two Numbers:
| 1 | 5 | |
| − | 1 | 0 |
| 5 |
