We are given a system of two linear equations: $5x - y = 8$ (1) $4x + 4y = 16$ (2) We need to solve the system and find the solution (x, y), or determine if there are infinitely many solutions, or no solutions.

1. Problem Description

We are given a system of two linear equations:

$5x - y = 8$ (1)

$4x + 4y = 16$ (2)

We need to solve the system and find the solution (x, y), or determine if there are infinitely many solutions, or no solutions.

2. Solution Steps

We can solve the system of equations using the substitution or elimination method. Let's use the elimination method. First, simplify equation (2) by dividing by 4:

$x + y = 4$ (3)

Now we can solve for $y$ in equation (3):

$y = 4 - x$ (4)

Substitute equation (4) into equation (1):

$5x - (4 - x) = 8$

$5x - 4 + x = 8$

$6x = 12$

$x = 2$

Now substitute $x = 2$ into equation (4):

$y = 4 - 2$

$y = 2$

So the solution is $(x, y) = (2, 2)$. Let's check this solution with the original equations:

Equation (1): $5(2) - 2 = 10 - 2 = 8$. Correct.

Equation (2): $4(2) + 4(2) = 8 + 8 = 16$. Correct.

The system has a unique solution.

3. Final Answer

A. The solution to the system is (2, 2).