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 = 25
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 = 25
Therefore, the two Numbers are 25 and 25
Note: Since the given Difference equals 0, the two Numbers are equal. And they are equal to the given Sum divided by 2,
Check Sum of the two Numbers:
25 + 25 = 50 ✓
Check Difference between the two Numbers:
25 − 25 = 0 ✓
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 =
50 + 0/2
x =
50/2
x = 25
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 =
50 − 0/2
y =
50/2
y = 25
Therefore, the two Numbers are 25 and 25
Note: Since the given Difference equals 0, the two Numbers are equal. And they are equal to the given Sum divided by 2,
Sum/2
.Check Sum of the two Numbers:
| 1 | ||
| 2 | 5 | |
| 2 | 5 | |
| 5 | 0 |
Check Difference between the two Numbers:
| 2 | 5 | |
| − | 2 | 5 |
| 0 |
