1. **State the problem:** We need to solve the system of equations by graphing: $$y = -\frac{6}{5}x$$ $$y = -\frac{2}{5}x + 4$$ 2. **Fill in the tables for each equation:** For $$y = -\frac{6}{5}x$$: - When $$x=0$$, $$y = -\frac{6}{5} \times 0 = 0$$ (correcting the given value from 1 to 0) - When $$x=5$$, $$y = -\frac{6}{5} \times 5 = -6$$ Table: $$\begin{array}{c|c} x & y \\\hline 0 & 0 \\ 5 & -6 \end{array}$$ For $$y = -\frac{2}{5}x + 4$$: - When $$x=0$$, $$y = -\frac{2}{5} \times 0 + 4 = 4$$ - When $$x=5$$, $$y = -\frac{2}{5} \times 5 + 4 = -2 + 4 = 2$$ Table: $$\begin{array}{c|c} x & y \\\hline 0 & 4 \\ 5 & 2 \end{array}$$ 3. **Graph the system:** - Plot points from both tables. - Draw the lines through these points. - The solution to the system is the intersection point of the two lines. 4. **Find the intersection algebraically:** Set the two expressions for $$y$$ equal: $$-\frac{6}{5}x = -\frac{2}{5}x + 4$$ Add $$\frac{2}{5}x$$ to both sides: $$-\frac{6}{5}x + \frac{2}{5}x = 4$$ Simplify: $$-\frac{6}{5}x + \frac{2}{5}x = -\frac{4}{5}x$$ So: $$-\frac{4}{5}x = 4$$ Divide both sides by $$-\frac{4}{5}$$: $$x = \frac{4}{-\frac{4}{5}} = 4 \times \left(-\frac{5}{4}\right) = -5$$ 5. **Find $$y$$ at $$x = -5$$:** Using $$y = -\frac{6}{5}x$$: $$y = -\frac{6}{5} \times (-5) = 6$$ 6. **Final answer:** The solution to the system is $$\boxed{(-5, 6)}$$. This means the two lines intersect at the point $$(-5, 6)$$.