1. **State the problem:** Solve the system of equations: $$\begin{aligned} 5x - 2y - 4 &= 0 \\ 3x + 16y - 54 &= 0 \end{aligned}$$ 2. **Rewrite each equation in standard form:** $$5x - 2y = 4$$ $$3x + 16y = 54$$ 3. **Use the elimination method to solve for one variable.** Multiply the first equation by 8 to align the coefficients of $y$: $$8(5x - 2y) = 8(4) \Rightarrow 40x - 16y = 32$$ 4. **Add the new equation to the second original equation:** $$\begin{aligned} 40x - 16y &= 32 \\ 3x + 16y &= 54 \end{aligned}$$ Adding: $$40x - 16y + 3x + 16y = 32 + 54$$ $$43x + \cancel{-16y + 16y} = 86$$ $$43x = 86$$ 5. **Solve for $x$:** $$x = \frac{86}{43} = 2$$ 6. **Substitute $x=2$ into one of the original equations to find $y$.** Using the first equation: $$5(2) - 2y = 4$$ $$10 - 2y = 4$$ 7. **Solve for $y$:** $$-2y = 4 - 10$$ $$-2y = -6$$ $$y = \frac{-6}{-2} = 3$$ **Final answer:** $$x = 2, \quad y = 3$$