1. **State the problem:** Solve the system of linear equations using substitution: $$x = 5y - 6$$ $$x + 5y = 2$$ 2. **Choose which expression to substitute:** The first equation already expresses $x$ in terms of $y$ as $x = 5y - 6$. This is easier to substitute into the second equation because $x$ is isolated. 3. **Substitute $x = 5y - 6$ into the second equation:** $$ (5y - 6) + 5y = 2 $$ 4. **Simplify and solve for $y$:** $$ 5y - 6 + 5y = 2 $$ $$ 10y - 6 = 2 $$ $$ 10y = 2 + 6 $$ $$ 10y = 8 $$ $$ y = \frac{\cancel{10}y}{\cancel{10}} = \frac{8}{10} = \frac{4}{5} $$ 5. **Substitute $y = \frac{4}{5}$ back into $x = 5y - 6$ to find $x$:** $$ x = 5 \times \frac{4}{5} - 6 $$ $$ x = 4 - 6 $$ $$ x = -2 $$ 6. **Final solution:** The ordered pair solution is $$\boxed{\left(-2, \frac{4}{5}\right)}$$. This means $x = -2$ and $y = \frac{4}{5}$ satisfy both equations.