Two Numbers with a Sum of 52 and a Difference of 8

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 =  30
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 =  22
Therefore, the two Numbers are 30 and 22
Check Sum of the two Numbers:

	3	0
	2	2
	5	2

30 + 22 = 52 ✓
Check Difference between the two Numbers:

	2	10
	3	0
−	2	2
		8

30 − 22 = 8 ✓