1. **State the problem:** Solve the system of linear equations: $$4.6t + 8.1u = 104$$ $$3.8t - 2.7u = -8$$ 2. **Choose a method:** We will use the elimination method to solve for $t$ and $u$. 3. **Eliminate one variable:** Multiply the first equation by 2.7 and the second by 8.1 to align coefficients of $u$: $$2.7(4.6t + 8.1u) = 2.7(104) \Rightarrow 12.42t + 21.87u = 280.8$$ $$8.1(3.8t - 2.7u) = 8.1(-8) \Rightarrow 30.78t - 21.87u = -64.8$$ 4. **Add the two equations to eliminate $u$:** $$12.42t + 21.87u + 30.78t - 21.87u = 280.8 - 64.8$$ $$ (12.42 + 30.78)t + \cancel{21.87u} - \cancel{21.87u} = 216$$ $$43.2t = 216$$ 5. **Solve for $t$:** $$t = \frac{216}{43.2}$$ $$t = 5$$ 6. **Substitute $t=5$ into the first original equation to find $u$:** $$4.6(5) + 8.1u = 104$$ $$23 + 8.1u = 104$$ 7. **Isolate $u$:** $$8.1u = 104 - 23$$ $$8.1u = 81$$ 8. **Solve for $u$:** $$u = \frac{81}{8.1}$$ $$u = 10$$ **Final answer:** $$t = 5, \quad u = 10$$