The problem asks us to solve the following system of linear equations for $x$ and $y$: $2x + 5y = 17$ (1) $5x + 8y = 11$ (2) Then, we need to determine the solution of the system.

1. Problem Description

The problem asks us to solve the following system of linear equations for $x$ and $y$:

$2x + 5y = 17$ (1)

$5x + 8y = 11$ (2)

Then, we need to determine the solution of the system.

2. Solution Steps

We can use the method of substitution or elimination. Let's use elimination.

Multiply equation (1) by 5 and equation (2) by 2:

$5(2x + 5y) = 5(17)$

$10x + 25y = 85$ (3)

$2(5x + 8y) = 2(11)$

$10x + 16y = 22$ (4)

Subtract equation (4) from equation (3):

$(10x + 25y) - (10x + 16y) = 85 - 22$

$10x + 25y - 10x - 16y = 63$

$9y = 63$

$y = \frac{63}{9}$

$y = 7$

Now substitute $y = 7$ into equation (1):

$2x + 5(7) = 17$

$2x + 35 = 17$

$2x = 17 - 35$

$2x = -18$

$x = \frac{-18}{2}$

$x = -9$

So the solution is $x = -9$ and $y = 7$. The ordered pair is $(-9, 7)$.

3. Final Answer

The solution to the system is $(-9, 7)$.

The answer is A. The solution to the system is $(-9, 7)$.