1. **Problem 1: Solve the system by equalization:** Given: $$y = 3x + 5$$ $$y = 2x + 2$$ 2. Since both expressions equal $y$, set them equal to each other: $$3x + 5 = 2x + 2$$ 3. Subtract $2x$ from both sides: $$3x + 5 - 2x = 2x + 2 - 2x$$ $$\cancel{3x} + 5 - \cancel{2x} = \cancel{2x} + 2 - \cancel{2x}$$ $$x + 5 = 2$$ 4. Subtract 5 from both sides: $$x + 5 - 5 = 2 - 5$$ $$x = -3$$ 5. Substitute $x = -3$ into one of the original equations to find $y$: $$y = 3(-3) + 5 = -9 + 5 = -4$$ **Final solution:** $$x = -3, \quad y = -4$$