1. **Stating the problem:** We need to solve the system of linear equations using the graphical method: $$\begin{cases} 3x - y = 4 \\ x = 4y - 17 \end{cases}$$ 2. **Rewrite each equation in terms of $y$ (to graph):** - From the first equation: $$3x - y = 4 \implies y = 3x - 4$$ - From the second equation: $$x = 4y - 17 \implies 4y = x + 17 \implies y = \frac{x + 17}{4} = \frac{1}{4}x + \frac{17}{4}$$ 3. **Interpretation:** - The first line has slope 3 and y-intercept -4. - The second line has slope $\frac{1}{4}$ and y-intercept $\frac{17}{4} = 4.25$. 4. **Find the point of intersection algebraically (since graphical method looks at where lines meet):** Set the two expressions for $y$ equal: $$3x - 4 = \frac{1}{4}x + \frac{17}{4}$$ Multiply both sides by 4 to clear denominators: $$4(3x - 4) = 4\left(\frac{1}{4}x + \frac{17}{4}\right) \implies 12x - 16 = x + 17$$ Bring terms together: $$12x - x = 17 + 16 \implies 11x = 33 \implies x = 3$$ Find $y$: $$y = 3(3) - 4 = 9 - 4 = 5$$ 5. **Final solution:** $$\boxed{(x,y) = (3,5)}$$ This is the point where the two lines intersect, solution of the system.