Final answer:
The solution to the system of equations using the addition method is x = 17 and y = 23.
Step-by-step explanation:
To solve the given system of equations using the addition method, we can add the two equations together to eliminate the variable y. Adding the equations, we get: (5x - 3y) + (-4x + 3y) = 12 + 5. This simplifies to x = 17.
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. Using the first equation, we substitute x = 17 and solve for y: 5(17) - 3y = 12. Simplifying this equation gives us y = 23.
Therefore, the solution to the system of equations is x = 17 and y = 23.