We are asked to solve the system of linear equations: $3s + 2t = 10$ (1) $4s - 6t = 9$ (2) using the elimination method. The solution should be in the form of an ordered pair $(s, t)$.

1. Problem Description

We are asked to solve the system of linear equations:

$3s + 2t = 10$ (1)

$4s - 6t = 9$ (2)

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

2. Solution Steps

We can eliminate $t$ by multiplying equation (1) by 3:

$3(3s + 2t) = 3(10)$

$9s + 6t = 30$ (3)

Now we add equation (3) and equation (2):

$(9s + 6t) + (4s - 6t) = 30 + 9$

$13s = 39$

$s = \frac{39}{13}$

$s = 3$

Now substitute $s=3$ into equation (1):

$3(3) + 2t = 10$

$9 + 2t = 10$

$2t = 10 - 9$

$2t = 1$

$t = \frac{1}{2}$

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

3. Final Answer

$(3, \frac{1}{2})$