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 = 61
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 = 56
Therefore, the two Numbers are 61 and 56
Check Sum of the two Numbers:
61 + 56 = 117 ✓
Check Difference between the two Numbers:
61 − 56 = 5 ✓
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 =
117 + 5/2
x =
122/2
x = 61
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 =
117 − 5/2
y =
112/2
y = 56
Therefore, the two Numbers are 61 and 56
Check Sum of the two Numbers:
| 1 | |||
| 6 | 1 | ||
| 5 | 6 | ||
| 1 | 1 | 7 |
Check Difference between the two Numbers:
| 5 | 11 | |
| 6 | 1 | |
| − | 5 | 6 |
| 5 |
