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 = 19
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 = 9
Therefore, the two Numbers are 19 and 9
Check Sum of the two Numbers:
19 + 9 = 28 ✓
Check Difference between the two Numbers:
19 − 9 = 10 ✓
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 =
28 + 10/2
x =
38/2
x = 19
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 =
28 − 10/2
y =
18/2
y = 9
Therefore, the two Numbers are 19 and 9
Check Sum of the two Numbers:
| 1 | ||
| 1 | 9 | |
| 9 | ||
| 2 | 8 |
Check Difference between the two Numbers:
| 1 | 9 | |
| − | 9 | |
| 1 | 0 |
