1. **State the problem:** Solve the system of equations: $$y=3x-2$$ $$4x+2y=6$$ 2. **Use substitution method:** Since $y$ is already expressed in terms of $x$ in the first equation, substitute $y=3x-2$ into the second equation. 3. **Substitute and simplify:** $$4x + 2(3x - 2) = 6$$ $$4x + 6x - 4 = 6$$ $$10x - 4 = 6$$ 4. **Solve for $x$:** $$10x = 6 + 4$$ $$10x = 10$$ $$x = \cancel{\frac{10}{10}}1$$ 5. **Find $y$ using $x=1$:** $$y = 3(1) - 2 = 3 - 2 = 1$$ 6. **Solution:** The solution to the system is $\boxed{(1,1)}$. 7. **Confirm by graphing:** The line $y=3x-2$ passes through $(1,1)$ and the line $4x+2y=6$ can be rewritten as: $$2y = 6 - 4x$$ $$y = 3 - 2x$$ At $x=1$, $y=3 - 2(1) = 1$, confirming the solution lies on both lines.