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Which statement is correct for the pair of inequalities 3x + 2y ≤ 6 and 6x + 4y ≥ 20?

1. The two graphs do not intersect
2. Neither graph includes the origin
3. Both graphs pass through the point (1, 1)
4. None of the above

Correct answer: The two graphs do not intersect

Solution

The boundary 6x+4y=20 is 3x+2y=10, parallel to 3x+2y=6, so the two boundary lines never intersect. The region 3x+2y<=6 contains the origin (0<=6), so 'neither includes origin' is false; (1,1) gives 5<=6 and 10>=20 (false), so it is not on both. Correct: the graphs do not intersect.

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