We are given a system of two linear equations: $5x - y = 8$ $4x + 4y = 16$ We need to solve this system and choose the correct solution option and the statement explaining the solution.

1. Problem Description

We are given a system of two linear equations:

$5x - y = 8$

$4x + 4y = 16$

We need to solve this system and choose the correct solution option and the statement explaining the solution.

2. Solution Steps

We can use the substitution or elimination method to solve the system. Let's use the elimination method. First, divide the second equation by 4:

$4x + 4y = 16 \implies x + y = 4$

Now we have:

$5x - y = 8$

$x + y = 4$

Add the two equations:

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

$6x = 12$

$x = \frac{12}{6}$

$x = 2$

Substitute $x = 2$ into the equation $x + y = 4$:

$2 + y = 4$

$y = 4 - 2$

$y = 2$

So the solution is $(x, y) = (2, 2)$.

Now, let's consider the second equation: $4x + 4y = 16$.

Dividing by 4 gives: $x + y = 4$.

Rewriting this as $y = 4 - x$.

The first equation is $5x - y = 8$.

Rewriting this as $y = 5x - 8$.

If the lines were the same, we could multiply the second equation by

5.

Now check if the solution is unique. Since we found only one solution $(2, 2)$, the graphs intersect at one point, so the solution is unique.

3. Final Answer

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

The graphs intersect at one point, so the solution is unique.