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 = 63
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 = 27
Therefore, the two Numbers are 63 and 27
Check Sum of the two Numbers:
63 + 27 = 90 ✓
Check Difference between the two Numbers:
63 − 27 = 36 ✓
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 =
90 + 36/2
x =
126/2
x = 63
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 =
90 − 36/2
y =
54/2
y = 27
Therefore, the two Numbers are 63 and 27
Check Sum of the two Numbers:
1 | ||
6 | 3 | |
2 | 7 | |
9 | 0 |
Check Difference between the two Numbers:
5 | 13 | |
6 | 3 | |
− | 2 | 7 |
3 | 6 |