Two Numbers with a Sum of 43 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 =  31
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 =  12
Therefore, the two Numbers are 31 and 12
Check Sum of the two Numbers:

	3	1
	1	2
	4	3

31 + 12 = 43 ✓
Check Difference between the two Numbers:

	2	11
	3	1
−	1	2
	1	9

31 − 12 = 19 ✓