1. **State the problem:** Solve the system of linear equations using the elimination method. Given the first system: $$28.\quad 2x = 11 - y$$ $$\frac{x}{5} + \frac{y}{4} = 1$$ 2. **Rewrite equations in standard form:** From the first equation: $$2x + y = 11$$ From the second equation multiply both sides by 20 (LCM of 5 and 4): $$4x + 5y = 20$$ 3. **Elimination method:** Multiply the first equation by 4 to align coefficients of $x$: $$8x + 4y = 44$$ Now subtract the second equation: $$8x + 4y = 44$$ $$-(4x + 5y = 20)$$ Gives: $$4x - y = 24$$ 4. **Solve for $y$:** $$4x - y = 24 \implies y = 4x - 24$$ 5. **Substitute $y$ back into one original equation:** Use $2x + y = 11$: $$2x + (4x - 24) = 11$$ $$6x - 24 = 11$$ $$6x = 35$$ $$x = \frac{35}{6}$$ 6. **Find $y$:** $$y = 4\times \frac{35}{6} - 24 = \frac{140}{6} - 24 = \frac{140}{6} - \frac{144}{6} = -\frac{4}{6} = -\frac{2}{3}$$ **Final solution:** $$x = \frac{35}{6}, \quad y = -\frac{2}{3}$$