To solve this system of equations using the method of addition, we will first rewrite the equations in standard form:

1) 7x + 4y = 74
2) 3x + 2y = 32

Next, we will multiply Equation 2 by 2 so that the coefficients of y in both equations become the same:

1) 7x + 4y = 74
2) 6x + 4y = 64

Now, we will subtract Equation 2 from Equation 1:

(7x + 4y) - (6x + 4y) = 74 - 64
7x + 4y - 6x - 4y = 10
x = 10

Now that we have found the value of x, we can substitute it back into either of the original equations to find the value of y. Let's use Equation 1:

7(10) + 4y = 74
70 + 4y = 74
4y = 4
y = 1

Therefore, the solution to the system of equations is x = 10 and y = 1.