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1) What is the value of y in the system x+3y-z=-3, 6x=2y-1 and x=z+3 IF x = 5/6 and z = 23/6?

2) Given the systems x+y+z=-14 and 2x+y+6z=16, how many number of solutions to the system are there?

  • Math -

    1. strange question

    Without looking at your last part of the given x and z values, just solving the system ....
    from the 2nd:
    2y = 6x+1
    y = (6x+1)/2

    from the 3rd:
    z = x-3

    back into the 1st:
    x + 3y - z = -3
    x + 3(6x+1)/2 - (x-3) = -3
    times 2
    2x + 18x + 3 - 2x + 6 = -6
    18x = -15
    x = -15/18 =-5/6

    then y = (6(-5/6) + 1)/2 = -2
    z = -5/6 - 3 = -23/6

    So there is one uniques solution of (-5/6, -2, -23/6)
    and the value of y is -2

    Now when you give an x value and a z value different from the actual solution, it will depend on which equation you sub into.
    There would be 3 different answers for the value of y

    2. Each equation represents a plane. Since the 2 planes are not parallel, they will intersect in a line.
    There will be an infinite number of points on that line, thus there will be an infinite number of solutions for your system.

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