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 = 74
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 = 71
Therefore, the two Numbers are 74 and 71
Check Sum of the two Numbers:
74 + 71 = 145 ✓
Check Difference between the two Numbers:
74 − 71 = 3 ✓
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 =
145 + 3/2
x =
148/2
x = 74
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 =
145 − 3/2
y =
142/2
y = 71
Therefore, the two Numbers are 74 and 71
Check Sum of the two Numbers:
| 1 | |||
| 7 | 4 | ||
| 7 | 1 | ||
| 1 | 4 | 5 |
Check Difference between the two Numbers:
| 7 | 4 | |
| − | 7 | 1 |
| 3 |
