1. **State the problem:** We are given a system of linear equations: $$x + 5y = -13$$ $$3x + 5y = -4$$ We need to solve for $x$ and $y$. 2. **Write down the system:** Equation 1: $x + 5y = -13$ Equation 2: $3x + 5y = -4$ 3. **Subtract Equation 1 from Equation 2 to eliminate $y$:** $$ (3x + 5y) - (x + 5y) = -4 - (-13) $$ $$ 3x + 5y - x - 5y = -4 + 13 $$ $$ (3x - x) + (5y - 5y) = 9 $$ $$ 2x + \cancel{5y - 5y} = 9 $$ $$ 2x = 9 $$ 4. **Solve for $x$:** $$ x = \frac{9}{2} $$ 5. **Substitute $x = \frac{9}{2}$ into Equation 1 to find $y$:** $$ \frac{9}{2} + 5y = -13 $$ 6. **Isolate $y$:** $$ 5y = -13 - \frac{9}{2} $$ $$ 5y = -\frac{26}{2} - \frac{9}{2} $$ $$ 5y = -\frac{35}{2} $$ 7. **Divide both sides by 5:** $$ y = \frac{-\frac{35}{2}}{5} = -\frac{35}{2} \times \frac{1}{5} = -\frac{35}{10} $$ $$ y = -\frac{7}{2} $$ **Final solution:** $$ x = \frac{9}{2}, \quad y = -\frac{7}{2} $$