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 = 95
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 = 46
Therefore, the two Numbers are 95 and 46
Check Sum of the two Numbers:
95 + 46 = 141 ✓
Check Difference between the two Numbers:
95 − 46 = 49 ✓
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 =
141 + 49/2
x =
190/2
x = 95
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 =
141 − 49/2
y =
92/2
y = 46
Therefore, the two Numbers are 95 and 46
Check Sum of the two Numbers:
| 1 | 1 | ||
| 9 | 5 | ||
| 4 | 6 | ||
| 1 | 4 | 1 |
Check Difference between the two Numbers:
| 8 | 15 | |
| 9 | 5 | |
| − | 4 | 6 |
| 4 | 9 |
