1. **State the problem:** Solve the system of equations by graphing: $$y - 5x = -26$$ $$y + 2x = 9$$ 2. **Rewrite each equation in slope-intercept form $y = mx + b$:** For the first equation: $$y - 5x = -26 \implies y = 5x - 26$$ For the second equation: $$y + 2x = 9 \implies y = -2x + 9$$ 3. **Graph the two lines:** - The first line has slope $5$ and y-intercept $-26$. - The second line has slope $-2$ and y-intercept $9$. 4. **Find the intersection point algebraically (since graphing is visual):** Set the right sides equal: $$5x - 26 = -2x + 9$$ 5. **Solve for $x$:** $$5x + 2x = 9 + 26$$ $$7x = 35$$ $$x = \frac{\cancel{7}x}{\cancel{7}} = \frac{35}{7} = 5$$ 6. **Substitute $x=5$ into one of the equations to find $y$:** Using $y = 5x - 26$: $$y = 5(5) - 26 = 25 - 26 = -1$$ 7. **Solution:** The lines intersect at the point $\boxed{(5, -1)}$. This is the solution to the system of equations.