1. **State the problem:** Solve the system of equations: $$x = y - 6$$ $$5x + 2y = -2$$ 2. **Substitute** the expression for $x$ from the first equation into the second: $$5(y - 6) + 2y = -2$$ 3. **Distribute** the 5: $$5y - 30 + 2y = -2$$ 4. **Combine like terms:** $$7y - 30 = -2$$ 5. **Add 30 to both sides:** $$7y - 30 + 30 = -2 + 30$$ $$7y = 28$$ 6. **Divide both sides by 7:** $$\cancel{7}y = \frac{28}{\cancel{7}}$$ $$y = 4$$ 7. **Substitute $y=4$ back into the first equation to find $x$:** $$x = 4 - 6$$ $$x = -2$$ **Final answer:** $$x = -2, \quad y = 4$$