1. **State the problem:** Solve the system of equations: $$x + y = 10$$ $$2x + 3y = 18$$ 2. **Use substitution or elimination method.** Here, we use substitution by solving the first equation for $y$: $$y = 10 - x$$ 3. **Substitute $y$ into the second equation:** $$2x + 3(10 - x) = 18$$ 4. **Simplify and solve for $x$:** $$2x + 30 - 3x = 18$$ $$\cancel{2x} + 30 - \cancel{3x} = 18$$ $$-x + 30 = 18$$ 5. **Isolate $x$:** $$-x = 18 - 30$$ $$-x = -12$$ $$x = 12$$ 6. **Substitute $x = 12$ back into $y = 10 - x$ to find $y$:** $$y = 10 - 12 = -2$$ 7. **Solution:** $$(x, y) = (12, -2)$$ This matches the third option given.