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 = 18
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 18 and 14
Check Sum of the two Numbers:
18 + 14 = 32 ✓
Check Difference between the two Numbers:
18 − 14 = 4 ✓
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 =
32 + 4/2
x =
36/2
x = 18
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 =
32 − 4/2
y =
28/2
y = 14
Therefore, the two Numbers are 18 and 14
Check Sum of the two Numbers:
| 1 | ||
| 1 | 8 | |
| 1 | 4 | |
| 3 | 2 |
Check Difference between the two Numbers:
| 1 | 8 | |
| − | 1 | 4 |
| 4 |
