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 = 24
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 = 11
Therefore, the two Numbers are 24 and 11
Check Sum of the two Numbers:
24 + 11 = 35 ✓
Check Difference between the two Numbers:
24 − 11 = 13 ✓
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 =
35 + 13/2
x =
48/2
x = 24
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 =
35 − 13/2
y =
22/2
y = 11
Therefore, the two Numbers are 24 and 11
Check Sum of the two Numbers:
| 2 | 4 | |
| 1 | 1 | |
| 3 | 5 |
Check Difference between the two Numbers:
| 2 | 4 | |
| − | 1 | 1 |
| 1 | 3 |
