Can a matrice be in row reduce form however its solution is a no solution?

A survey of 500 high school students was taken to determine their favorite chocolate candy. Of the 500 students surveyed, 159 like Snickers, 151 like Twix, 176 like Reese s Peanut Butter Cups, 90 like Snickers and Twix, 99 like Twix and Reese s Peanut Butter Cups, 108 like Snickers and Reese s Peanut Butter Cups, and 56 like all three kinds of chocolate candy. How many students like no more than one kind of these chocolate candies?

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