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