Two Numbers with a Sum of 35 and a Difference of 19

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 =  27
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 =  8
Therefore, the two Numbers are 27 and 8
Check Sum of the two Numbers:

	1
	2	7
		8
	3	5

27 + 8 = 35 ✓
Check Difference between the two Numbers:

	1	17
	2	7
−		8
	1	9

27 − 8 = 19 ✓