1. **State the problem:** Solve the system of equations: $$3x + 2y = 18$$ $$4x - y = 2$$ 2. **Choose a method:** We will use substitution or elimination. Here, let's use substitution. 3. **Isolate $y$ in the second equation:** $$4x - y = 2 \implies y = 4x - 2$$ 4. **Substitute $y$ into the first equation:** $$3x + 2(4x - 2) = 18$$ 5. **Simplify and solve for $x$:** $$3x + 8x - 4 = 18$$ $$11x - 4 = 18$$ $$11x = 18 + 4$$ $$11x = 22$$ $$x = \frac{22}{11}$$ $$x = 2$$ 6. **Substitute $x=2$ back into $y = 4x - 2$ to find $y$:** $$y = 4(2) - 2$$ $$y = 8 - 2$$ $$y = 6$$ 7. **Final answer:** $$\boxed{(x, y) = (2, 6)}$$