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 = 32
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 = 21
Therefore, the two Numbers are 32 and 21
Check Sum of the two Numbers:
32 + 21 = 53 ✓
Check Difference between the two Numbers:
32 − 21 = 11 ✓
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 =
53 + 11/2
x =
64/2
x = 32
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 =
53 − 11/2
y =
42/2
y = 21
Therefore, the two Numbers are 32 and 21
Check Sum of the two Numbers:
| 3 | 2 | |
| 2 | 1 | |
| 5 | 3 |
Check Difference between the two Numbers:
| 3 | 2 | |
| − | 2 | 1 |
| 1 | 1 |
