Algebra

Find the coordinates of the vertices of the figures formed by y -< x + 2, x + 2 -< 6, and y >- -2
A)(0,0),(2,4),(8,-2)
B)(-4,-2),(2,4),(8,-2)
C)(-4,-2),(4,2),(8,-2)
D)(-2,-4),(2,4),(8,-2)
I chose B

this one confused me this is all the work to show:
-2 -< -4 + 2
2 + 4 -< 6
-2

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asked by Jon
  1. the way u did it, if I try to do the others, Aren't they all true though?

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    posted by Rudy
  2. No, all are not true

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    posted by Jon
  3. We have this:

    (y -< x + 2) = point 1.

    (x + 2 -< 6) = point 2.

    (y >- -2) = point 3.

    Replace all inequality symbols with an equal sign for easy simplification.

    Point 3:

    y >- -2 becomes y = -2

    We just found y.

    We plug y = -2 in point 1 to find x.

    -2 = x + 2

    -2 - 2 = x

    -4 = x

    We know that y = -2 and x = -4.

    ================================

    Notice that the next point to follow in choice B is (2,4), where x = 2 and y = 4.

    We plug that into all three points to see if we get a true statement.

    (y -< x + 2) = point 1.

    4 -< 2 + 2...true statement

    (x + 2 -< 6) = point 2.

    2 + 4 -< 6...true statement

    (y >- -2) = point 3.

    4 >- -2...true statement

    So far, it appears that choice B is correct.

    ===================================

    What is the next point given in choice B? It is point (8, -2).

    We do the same-->plug to check for true statement.

    (y -< x + 2) = point 1.

    -2 -< 8 + 2...true statement

    (x + 2 -< 6) = point 2.

    8 + 2 -< 6...false statement

    (y >- -2) = point 3.

    -2 >- -2...true statement

    We know that choice A and D cannot be the answers. We just found out that choice B is most likely not the answer because of the false statement.

    I would say the answer is choice C.

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    posted by Guido

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