Math

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Given the following system is consistent

x+y=1
tx+y=t
(1+t)x+2y=3

Find the exact value of t.

  • Math -

    subtract the first from the second
    xt - x = t-1
    x(t-1) = t-1
    x = 1, if t±1

    in 1st:
    1+y = 1
    y = 0
    in the last:
    (1+t)(1) + 0 = 3
    1+t = 3
    t = 2

  • Math -

    Subtracting the first equation from the second gives you:
    t-1 = (t-1)x
    Therefore x = 1.
    The first equation tells you that y = 0.
    The third equation requires that
    1 + t = 3
    t = 2

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