We are given a system of two linear equations with two variables, $t$ and $u$: $6t - 9u = 10$ $2t + 3u = 4$ We need to solve for $t$ and $u$.

1. Problem Description

We are given a system of two linear equations with two variables, $t$ and $u$:

$6t - 9u = 10$

$2t + 3u = 4$

We need to solve for $t$ and $u$.

2. Solution Steps

We can solve this system of equations using substitution or elimination. Let's use elimination.

Multiply the second equation by 3:

$3(2t + 3u) = 3(4)$

$6t + 9u = 12$

Now we have:

$6t - 9u = 10$

$6t + 9u = 12$

Add the two equations together:

$(6t - 9u) + (6t + 9u) = 10 + 12$

$12t = 22$

Solve for $t$:

$t = \frac{22}{12} = \frac{11}{6}$

Substitute $t = \frac{11}{6}$ into the second original equation:

$2(\frac{11}{6}) + 3u = 4$

$\frac{11}{3} + 3u = 4$

$3u = 4 - \frac{11}{3} = \frac{12}{3} - \frac{11}{3} = \frac{1}{3}$

$u = \frac{1}{3} \div 3 = \frac{1}{3} \times \frac{1}{3} = \frac{1}{9}$

Thus, $t = \frac{11}{6}$ and $u = \frac{1}{9}$.

3. Final Answer

$t = \frac{11}{6}$

$u = \frac{1}{9}$