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 = 29
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 = 18
Therefore, the two Numbers are 29 and 18
Check Sum of the two Numbers:
29 + 18 = 47 ✓
Check Difference between the two Numbers:
29 − 18 = 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 =
47 + 11/2
x =
58/2
x = 29
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 =
47 − 11/2
y =
36/2
y = 18
Therefore, the two Numbers are 29 and 18
Check Sum of the two Numbers:
| 1 | ||
| 2 | 9 | |
| 1 | 8 | |
| 4 | 7 |
Check Difference between the two Numbers:
| 2 | 9 | |
| − | 1 | 8 |
| 1 | 1 |
