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 = 8
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 8 and 5
Check Sum of the two Numbers:
8 + 5 = 13 ✓
Check Difference between the two Numbers:
8 − 5 = 3 ✓
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 =
13 + 3/2
x =
16/2
x = 8
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 =
13 − 3/2
y =
10/2
y = 5
Therefore, the two Numbers are 8 and 5
Check Sum of the two Numbers:
| 1 | ||
| 8 | ||
| 5 | ||
| 1 | 3 |
Check Difference between the two Numbers:
| 8 | |
| − | 5 |
| 3 |
