1. Let's start with a basic substitution problem: Solve the system of equations using substitution. Given: $$\begin{cases} y = 2x + 3 \\ 3x + y = 9 \end{cases}$$ 2. The substitution method involves replacing one variable with an expression from the other equation. 3. From the first equation, we already have $y$ expressed in terms of $x$: $y = 2x + 3$. 4. Substitute $y = 2x + 3$ into the second equation: $$3x + (2x + 3) = 9$$ 5. Simplify and solve for $x$: $$3x + 2x + 3 = 9$$ $$5x + 3 = 9$$ $$5x = 9 - 3$$ $$5x = 6$$ $$x = \frac{6}{5}$$ 6. Substitute $x = \frac{6}{5}$ back into $y = 2x + 3$ to find $y$: $$y = 2 \times \frac{6}{5} + 3 = \frac{12}{5} + 3 = \frac{12}{5} + \frac{15}{5} = \frac{27}{5}$$ 7. Final solution: $$\boxed{\left( \frac{6}{5}, \frac{27}{5} \right)}$$ This means the point $(\frac{6}{5}, \frac{27}{5})$ satisfies both equations.