1. **Stating the problem:** You want to solve a system of equations graphically by using substitution. 2. **Formula and rules:** Substitution involves solving one equation for one variable and then substituting that expression into the other equation. 3. **Step-by-step process:** 1. Solve one of the equations for one variable, for example, solve for $y$ in terms of $x$. 2. Substitute this expression for $y$ into the other equation. 3. Simplify and solve the resulting equation for $x$. 4. Substitute the found $x$ value back into the expression for $y$ to find the corresponding $y$ value. 5. The solution $(x,y)$ is the point where the two graphs intersect. 4. **Example:** Given the system: $$\begin{cases} y = 2x + 3 \\ 3x + y = 9 \end{cases}$$ - Step 1: The first equation is already solved for $y$. - Step 2: Substitute $y = 2x + 3$ into the second equation: $$3x + (2x + 3) = 9$$ - Step 3: Simplify and solve for $x$: $$3x + 2x + 3 = 9$$ $$5x + 3 = 9$$ $$5x = 6$$ $$x = \frac{6}{5}$$ - Step 4: Substitute $x = \frac{6}{5}$ back into $y = 2x + 3$: $$y = 2 \times \frac{6}{5} + 3 = \frac{12}{5} + 3 = \frac{12}{5} + \frac{15}{5} = \frac{27}{5}$$ - Step 5: The solution is $\left(\frac{6}{5}, \frac{27}{5}\right)$. 5. **Interpretation:** This point is where the two graphs intersect, meaning it satisfies both equations. This method works well for linear systems and can be extended to nonlinear systems with more complex algebra.