Let c be a constant. For what values of c can the simultaneous equations x – y = 2; cx + y = 3 have a solution (x, y) inside quadrant I

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  1. we need x>0 and y>0
    eliminating y, we have

    x-(3-cx) = 2
    (c+1)x = 5
    c+1 > 0
    c > -1

    eliminating x, we have

    cx-cy = 2c
    cx+y = 3

    (1+c)y = 3-2c
    y = (3-2c)/(c+1)
    since c+1 > 0, 3-2c > 0, so c < 3/2

    so, -1 < c < 3/2

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    posted by Steve

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