1. **State the problem:** Solve the system of equations using the elimination method: $$2x + y = 7$$ $$x + 3y = 11$$ 2. **Write both equations clearly:** Equation 1: $2x + y = 7$ Equation 2: $x + 3y = 11$ 3. **Choose a variable to eliminate:** Let's eliminate $x$. 4. **Multiply equations to match coefficients of $x$:** Multiply Equation 2 by 2: $$2(x + 3y) = 2(11)$$ $$2x + 6y = 22$$ 5. **Subtract Equation 1 from the new equation to eliminate $x$:** $$\cancel{2x} + 6y - (\cancel{2x} + y) = 22 - 7$$ $$6y - y = 15$$ $$5y = 15$$ 6. **Solve for $y$:** $$y = \frac{15}{5} = 3$$ 7. **Substitute $y=3$ back into one of the original equations to find $x$:** Using Equation 1: $$2x + 3 = 7$$ $$2x = 7 - 3 = 4$$ $$x = \frac{4}{2} = 2$$ 8. **Final answer:** $$(x, y) = (2, 3)$$