1. **State the problem:** Solve the system of linear equations: $$10x + 4y = 15$$ $$15x - 8y = 33$$ 2. **Formula and method:** We will use the elimination method to solve for $x$ and $y$. The goal is to eliminate one variable by making the coefficients of $y$ (or $x$) opposites. 3. **Eliminate $y$:** Multiply the first equation by 2 to match the coefficient of $y$ in the second equation: $$2(10x + 4y) = 2(15) \Rightarrow 20x + 8y = 30$$ 4. **Add the new equation to the second equation:** $$20x + 8y = 30$$ $$15x - 8y = 33$$ Adding gives: $$20x + 8y + 15x - 8y = 30 + 33$$ $$35x = 63$$ 5. **Solve for $x$:** $$x = \frac{63}{35} = \frac{9}{5} = 1.8$$ 6. **Substitute $x=1.8$ into the first original equation:** $$10(1.8) + 4y = 15$$ $$18 + 4y = 15$$ 7. **Solve for $y$:** $$4y = 15 - 18 = -3$$ $$y = \frac{-3}{4} = -0.75$$ **Final answer:** $$x = 1.8, \quad y = -0.75$$