Two Numbers with a Sum of 55 and a Difference of 9

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 =  

Sum + Difference/2

Find x by substituting given Sum and Difference into equation for x and simplify:
x =  
x =  
x =  32
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 =  
y =  
y =  23
Therefore, the two Numbers are 32 and 23
Check Sum of the two Numbers:

	3	2
	2	3
	5	5

32 + 23 = 55 ✓
Check Difference between the two Numbers:

	2	12
	3	2
−	2	3
		9

32 − 23 = 9 ✓