Which point gives the graphical solution of (2x+y=9) and (x+y=5)?

Correct answer: ((4,1))

The direct answer is option B, (4,1). A graphical solution is the point where both lines meet, so the point must satisfy both equations. Subtract x+y=5 from 2x+y=9: x=4. Substitute x=4 into x+y=5: 4+y=5, so y=1. Therefore the intersection is (4,1). Checking both equations gives 2(4)+1=9 and 4+1=5. Option A, (3,2), satisfies x+y=5 but gives 2x+y=8, not 9. Option B satisfies both, so it is correct. Option C, (2,3), satisfies x+y=5 but gives 7 in the first equation. Option D, (1,4), satisfies x+y=5 but gives 6 in the first equation. The graph would show both lines crossing at the same ordered pair. Memory cue: test both coordinates in both equations, not just one.