In a class, the total number of students in two groups is (74), and the first group has (16) more students than the second. What will be the graphical solution?

Correct answer: ((45,29))

The direct answer is option A: the graphical solution is (45,29), where the first coordinate represents the first group and the second coordinate represents the second group. Let the numbers of students be x and y. The total gives x+y=74. Since the first group has 16 more students, x-y=16. Adding these equations gives 2x=90, so x=45. Substituting in x+y=74 gives 45+y=74, hence y=29. Therefore the two lines meet at (45,29), which is their common solution. Option A is correct because it satisfies both equations: 45+29=74 and 45-29=16. Option B gives (29,45); its total is 74, but the first group is 16 fewer, not 16 more, so it reverses the groups. Option C gives (44,30); its total is 74, but the difference is only 14, so it fails the second condition. Option D gives (46,28); its difference is 18, not 16, although its total is 74. In a graph, the intersection point represents the ordered pair satisfying both lines. Memory cue: add the equations to find the first variable, and remember that the first coordinate belongs to the first group.