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  1. option 2 is correct.

    step-by-step explanation:

    we are given two inequality equation

    x+y> 5 and -3x+2y< -2

    first we draw the graph of both function using t-table method

    equation: x+y> 5

    for x=0, y=5

    for x=-5, y=0

    table:

    x   :   0     5

    y   :   5     0

    test point (0,0) , 0> 5

    false

    equation: -3x+2y< -2

    for x=0, y=-1

    for x=2, y=4

    table:

    x   :   0     2

    y   : -1       4

    test point (0,0) , 0< -2

    true

    now we draw the graph. see the attachment for graph.

    common region would be solution set.

    option 2 is correct.

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