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 = 11
Therefore, the two Numbers are 18 and 11
Check Sum of the two Numbers:
18 + 11 = 29 ✓
Check Difference between the two Numbers:
18 − 11 = 7 ✓
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 =
29 + 7/2
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 =
29 − 7/2
y =
22/2
y = 11
Therefore, the two Numbers are 18 and 11
Check Sum of the two Numbers:
| 1 | 8 | |
| 1 | 1 | |
| 2 | 9 |
Check Difference between the two Numbers:
| 1 | 8 | |
| − | 1 | 1 |
| 7 |
