1. **State the problem:** Solve the system of equations for $y$ in terms of $x$: $$0 = -2y + 10 - 6x$$ $$14 - 22y = 18x$$ 2. **Rewrite the first equation to isolate $y$:** $$0 = -2y + 10 - 6x$$ $$-2y = -10 + 6x$$ $$y = \frac{-10 + 6x}{-2}$$ 3. **Simplify the expression for $y$:** $$y = \frac{\cancel{-10} + 6x}{\cancel{-2}} = \frac{10 - 6x}{2}$$ 4. **Rewrite the second equation and isolate $y$:** $$14 - 22y = 18x$$ $$-22y = 18x - 14$$ $$y = \frac{18x - 14}{-22}$$ 5. **Simplify the expression for $y$ in the second equation:** $$y = \frac{\cancel{18x} - 14}{\cancel{-22}} = -\frac{18x - 14}{22} = -\frac{18x}{22} + \frac{14}{22}$$ 6. **Simplify fractions:** $$y = -\frac{9x}{11} + \frac{7}{11}$$ 7. **Final expressions for $y$ from both equations:** From equation 1: $$y = \frac{10 - 6x}{2} = 5 - 3x$$ From equation 2: $$y = -\frac{9x}{11} + \frac{7}{11}$$ These are the expressions for $y$ in terms of $x$ from each equation.