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 = 30
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 = 15
Therefore, the two Numbers are 30 and 15
Check Sum of the two Numbers:
30 + 15 = 45 ✓
Check Difference between the two Numbers:
30 − 15 = 15 ✓
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 =
45 + 15/2
x =
60/2
x = 30
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 =
45 − 15/2
y =
30/2
y = 15
Therefore, the two Numbers are 30 and 15
Check Sum of the two Numbers:
| 3 | 0 | |
| 1 | 5 | |
| 4 | 5 |
Check Difference between the two Numbers:
| 2 | 10 | |
| 3 | 0 | |
| − | 1 | 5 |
| 1 | 5 |
