Two Numbers with a Sum of 55 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 =  37
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 =  18
Therefore, the two Numbers are 37 and 18
Check Sum of the two Numbers:

	1
	3	7
	1	8
	5	5

37 + 18 = 55 ✓
Check Difference between the two Numbers:

	2	17
	3	7
−	1	8
	1	9

37 − 18 = 19 ✓