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Find the point of intersection of the boundary lines of the inequalities 2x + y ≥ 2 and x - y ≤ 3, which gives the vertex of their common graph.

1. (0, 0)
2. (5/3, -4/3)
3. (5/3, 4/3)
4. (-4/3, 5/3)

Correct answer: (5/3, -4/3)

Solution

Solving 2x+y=2 and x-y=3 simultaneously: adding gives 3x=5 (after substitution x-y=3 -> y=x-3), so 2x+(x-3)=2 -> 3x=5 -> x=5/3, y=5/3-3=-4/3. Intersection (5/3, -4/3).

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