1. **State the problem:** Solve the system of linear equations: $$5 \cdot 26 = 2x + 5y$$ $$8 = 5x + 3y$$ 2. **Rewrite the first equation:** Calculate $5 \cdot 26$ first: $$130 = 2x + 5y$$ 3. **Express one variable from the second equation:** From $$8 = 5x + 3y$$ solve for $x$: $$5x = 8 - 3y$$ $$x = \frac{8 - 3y}{5}$$ 4. **Substitute $x$ into the first equation:** $$130 = 2\left(\frac{8 - 3y}{5}\right) + 5y$$ 5. **Multiply both sides by 5 to clear the denominator:** $$5 \cdot 130 = 5 \cdot \left(2 \cdot \frac{8 - 3y}{5} + 5y\right)$$ $$650 = 2(8 - 3y) + 25y$$ 6. **Expand and simplify:** $$650 = 16 - 6y + 25y$$ $$650 = 16 + 19y$$ 7. **Isolate $y$:** $$650 - 16 = 19y$$ $$634 = 19y$$ 8. **Divide both sides by 19:** $$y = \frac{634}{19}$$ Show cancellation: $$y = \frac{\cancel{634}}{\cancel{19}}$$ Calculate: $$y = 33.3684$$ 9. **Substitute $y$ back to find $x$:** $$x = \frac{8 - 3(33.3684)}{5}$$ $$x = \frac{8 - 100.1052}{5}$$ $$x = \frac{-92.1052}{5}$$ $$x = -18.4210$$ **Final answer:** $$x \approx -18.4210, \quad y \approx 33.3684$$