We are asked to find the solution to the system of equations: $5s + 3t = 11$ (1) $9s - 6t = 16$ (2) using the addition (elimination) method. The solution should be in the form of an ordered pair $(s, t)$.

1. Problem Description

We are asked to find the solution to the system of equations:

$5s + 3t = 11$ (1)

$9s - 6t = 16$ (2)

using the addition (elimination) method. The solution should be in the form of an ordered pair $(s, t)$.

2. Solution Steps

To eliminate the variable $t$, we can multiply equation (1) by 2:

$2(5s + 3t) = 2(11)$

$10s + 6t = 22$ (3)

Now, we can add equation (3) and equation (2) to eliminate $t$:

$(10s + 6t) + (9s - 6t) = 22 + 16$

$19s = 38$

$s = \frac{38}{19}$

$s = 2$

Now that we have found $s$, we can substitute it into either equation (1) or (2) to solve for $t$. Let's use equation (1):

$5(2) + 3t = 11$

$10 + 3t = 11$

$3t = 11 - 10$

$3t = 1$

$t = \frac{1}{3}$

So the solution is $(s, t) = (2, \frac{1}{3})$.

3. Final Answer

$(2, 1/3)$