The sum of a number and 5 times a second number is represented by the equation a+5b=19 . the sum of half of the first number and twice the second number is represented by 12a+2b=8 . what is the first number (a) and what is the second number (b)

Here you have a system of 2 equations and 2 unknowns. An easy way to solve this type is to isolate one of the variables.

12a + 2b = 8
2b = 8 - 12a
b =

b = 4 - 6a

Now plug 4 - 6a into equation 1 to solve for a.

a + 5(4 - 6a) = 19

a + 20 - 30a = 19

-29a = -1

a = 1/29 (answer)

Now plug a into the equation for b

b= 4 - 6(1/29)

b= 110/29 (answer)