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 = 144
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 = 93
Therefore, the two Numbers are 144 and 93
Check Sum of the two Numbers:
144 + 93 = 237 ✓
Check Difference between the two Numbers:
144 − 93 = 51 ✓
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 =
237 + 51/2
x =
288/2
x = 144
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 =
237 − 51/2
y =
186/2
y = 93
Therefore, the two Numbers are 144 and 93
Check Sum of the two Numbers:
| 1 | |||
| 1 | 4 | 4 | |
| 9 | 3 | ||
| 2 | 3 | 7 |
Check Difference between the two Numbers:
| 0 | 14 | ||
| 1 | 4 | 4 | |
| − | 9 | 3 | |
| 5 | 1 |
