Two Numbers with a Sum of 100 and a Difference of 34

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 =  67
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 =  33
Therefore, the two Numbers are 67 and 33
Check Sum of the two Numbers:

	1	1
		6	7
		3	3
	1	0	0

67 + 33 = 100 ✓
Check Difference between the two Numbers:

	6	7
−	3	3
	3	4

67 − 33 = 34 ✓