Final answer:
The values of the variables 'a' and 'b' are 8 and 5 respectively.
Step-by-step explanation:
The question is asking for the values of variables 'a' and 'b' given that the difference between them is 3 and their sum is 13. We can set up two equations using these conditions:
a - b = 3
a + b = 13
We can solve this system of equations by adding the two equations together to eliminate 'b':
(a - b) + (a + b) = 3 + 13
2a = 16
a = 8
We can substitute the value of 'a' back into one of the equations to find 'b':
8 + b = 13
b = 5
Therefore, the numbers are a = 8 and b = 5.