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 = 86
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 = 13
Therefore, the two Numbers are 86 and 13
Check Sum of the two Numbers:
86 + 13 = 99 ✓
Check Difference between the two Numbers:
86 − 13 = 73 ✓
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 =
99 + 73/2
x =
172/2
x = 86
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 =
99 − 73/2
y =
26/2
y = 13
Therefore, the two Numbers are 86 and 13
Check Sum of the two Numbers:
| 8 | 6 | |
| 1 | 3 | |
| 9 | 9 |
Check Difference between the two Numbers:
| 8 | 6 | |
| − | 1 | 3 |
| 7 | 3 |
