1. **State the problem:** Solve the system of linear equations: $$2x + 3y = 16.9$$ $$5x = y + 7.4$$ 2. **Rewrite the second equation to express $y$ in terms of $x$: ** $$5x = y + 7.4 \implies y = 5x - 7.4$$ 3. **Substitute $y = 5x - 7.4$ into the first equation:** $$2x + 3(5x - 7.4) = 16.9$$ 4. **Distribute and simplify:** $$2x + 15x - 22.2 = 16.9$$ 5. **Combine like terms:** $$17x - 22.2 = 16.9$$ 6. **Add 22.2 to both sides:** $$17x - \cancel{22.2} + \cancel{22.2} = 16.9 + 22.2$$ $$17x = 39.1$$ 7. **Divide both sides by 17 to solve for $x$:** $$\frac{17x}{\cancel{17}} = \frac{39.1}{\cancel{17}}$$ $$x = 2.3$$ 8. **Substitute $x = 2.3$ back into $y = 5x - 7.4$ to find $y$:** $$y = 5(2.3) - 7.4 = 11.5 - 7.4 = 4.1$$ 9. **Final solution rounded to the nearest tenth:** $$x = 2.3, \quad y = 4.1$$