1. The problem asks: What must be true for a system of linear equations to have no solution? 2. The system given is: $$y=\frac{1}{2}x - 7$$ $$y=\frac{1}{3}x - 7$$ 3. Recall that for two lines to have no solution (i.e., no point of intersection), they must be parallel but not the same line. 4. Parallel lines have equal slopes but different y-intercepts. 5. Let's analyze the options: - A: Slopes equal and y-intercepts not equal. This means lines are parallel and distinct, so no solution. - B: Slopes not equal. Lines intersect at one point, so one solution. - C: Slopes equal and y-intercepts equal. Lines coincide, so infinite solutions. 6. Therefore, the correct condition for no solution is option A. Final answer: **A. The slopes must be equal and the y-intercepts must not be equal.**