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 = 38
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 = 19
Therefore, the two Numbers are 38 and 19
Check Sum of the two Numbers:
38 + 19 = 57 ✓
Check Difference between the two Numbers:
38 − 19 = 19 ✓
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 =
57 + 19/2
x =
76/2
x = 38
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 =
57 − 19/2
y =
38/2
y = 19
Therefore, the two Numbers are 38 and 19
Check Sum of the two Numbers:
| 1 | ||
| 3 | 8 | |
| 1 | 9 | |
| 5 | 7 |
Check Difference between the two Numbers:
| 2 | 18 | |
| 3 | 8 | |
| − | 1 | 9 |
| 1 | 9 |
