1. **Problem statement:** Classify the system of linear equations based on the graph and find the solution. 2. **Recall:** - A system with two lines intersecting at one point has a unique solution. - Parallel lines have no solution. - Coincident lines have infinitely many solutions. 3. **(a) Intersecting lines:** Equations: $$y=\frac{1}{3}x$$ $$y=-2x+4$$ To find the solution, set the right sides equal: $$\frac{1}{3}x = -2x + 4$$ Multiply both sides by 3: $$x = -6x + 12$$ Add $6x$ to both sides: $$7x = 12$$ Divide by 7: $$x = \frac{12}{7}$$ Substitute back to find $y$: $$y = \frac{1}{3} \times \frac{12}{7} = \frac{12}{21} = \frac{4}{7}$$ Solution: $$\left(\frac{12}{7}, \frac{4}{7}\right)$$ 4. **(b) Parallel lines:** Equations: $$y=\frac{1}{3}x + 1$$ $$y=\frac{1}{3}x - 1$$ Since slopes are equal but intercepts differ, lines are parallel. No solution. 5. **(c) Coincident lines:** Equations: $$y=2x - 1$$ $$y=2x - 1$$ Lines are identical. Infinite solutions. **Final answers:** (a) Unique solution: $$\left(\frac{12}{7}, \frac{4}{7}\right)$$ (b) No solution. (c) Infinite solutions.