1. **State the problem:** We are given a system of linear equations represented by two lines on a graph. We need to determine the truth of statements about the lines: whether they are parallel, intersecting, and the number of solutions. 2. **Recall key concepts:** - Two lines are parallel if their slopes are equal. - If lines intersect at exactly one point, the system has one unique solution. - If lines do not intersect (are parallel and distinct), the system has no solution. 3. **Analyze the graph description:** - One line passes from bottom-left to top-right, indicating a positive slope. - The other line passes from top-left to bottom-right, indicating a negative slope. - The lines intersect approximately near the point $(2, 2)$. 4. **Interpret the statements:** **a. The lines are not parallel, so the system has one solution.** - Since the slopes are different (one positive, one negative), the lines are not parallel. - Therefore, they intersect at exactly one point. - This statement is **True**. **b. The lines do not intersect, so the system has no solution.** - The graph shows the lines intersecting near $(2, 2)$. - Therefore, this statement is **False**. **c. There is exactly one solution to the system of equations.** - Since the lines intersect at one point, the system has exactly one solution. - This statement is **True**. **d. The slopes of the lines are different.** - One line has a positive slope, the other a negative slope. - Therefore, the slopes are different. - This statement is **True**. **Final answers:** - a: True - b: False - c: True - d: True