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 = 73
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 = 57
Therefore, the two Numbers are 73 and 57
Check Sum of the two Numbers:
73 + 57 = 130 ✓
Check Difference between the two Numbers:
73 − 57 = 16 ✓
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 =
130 + 16/2
x =
146/2
x = 73
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 =
130 − 16/2
y =
114/2
y = 57
Therefore, the two Numbers are 73 and 57
Check Sum of the two Numbers:
| 1 | 1 | ||
| 7 | 3 | ||
| 5 | 7 | ||
| 1 | 3 | 0 |
Check Difference between the two Numbers:
| 6 | 13 | |
| 7 | 3 | |
| − | 5 | 7 |
| 1 | 6 |
