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 = 13
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 = 6
Therefore, the two Numbers are 13 and 6
Check Sum of the two Numbers:
13 + 6 = 19 ✓
Check Difference between the two Numbers:
13 − 6 = 7 ✓
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 =
19 + 7/2
x =
26/2
x = 13
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 =
19 − 7/2
y =
12/2
y = 6
Therefore, the two Numbers are 13 and 6
Check Sum of the two Numbers:
| 1 | 3 | |
| 6 | ||
| 1 | 9 |
Check Difference between the two Numbers:
| 0 | 13 | |
| 1 | 3 | |
| − | 6 | |
| 7 |
