1. The problem is to solve a system of equations by substitution. 2. The substitution method involves solving one equation for one variable and then substituting that expression into the other equation. 3. For example, if we have the system: $$\begin{cases} y = 2x + 3 \\ 3x + y = 9 \end{cases}$$ We can substitute $y$ from the first equation into the second. 4. Substitute $y = 2x + 3$ into $3x + y = 9$: $$3x + (2x + 3) = 9$$ 5. Simplify and solve for $x$: $$3x + 2x + 3 = 9$$ $$5x + 3 = 9$$ $$5x = 6$$ $$x = \frac{6}{5}$$ 6. Substitute $x = \frac{6}{5}$ back into $y = 2x + 3$: $$y = 2 \times \frac{6}{5} + 3 = \frac{12}{5} + 3 = \frac{12}{5} + \frac{15}{5} = \frac{27}{5}$$ 7. The solution to the system is: $$\left( \frac{6}{5}, \frac{27}{5} \right)$$