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Math Help - system of equations

  1. #1
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    system of equations

    For what value of the real number t have the system of equations

    tx+3y-1=0
    4x-y-2=0

    a, a soulotion
    b, infinitely many solutions
    c, no solutions

    Some help would be great, thanks!
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  2. #2
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    Re: system of equations

    Quote Originally Posted by sunnshine345 View Post
    For what value of the real number t have the system of equations
    tx+3y-1=0
    4x-y-2=0
    a, a soulotion
    b, infinitely many solutions
    c, no solutions
    It would be nice of you to show of your work and tell us what you don't understand.
    Otherwise, we are left guessing as to what you need.
    Thanks from topsquark
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  3. #3
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    Re: system of equations

    Quote Originally Posted by sunnshine345 View Post
    For what value of the real number t have the system of equations

    tx+3y-1=0
    4x-y-2=0

    a, a soulotion
    b, infinitely many solutions
    c, no solutions

    Some help would be great, thanks!
    A system of n linear equations in n unknowns has no solution, one solution, or infinitely many solutions. This is ALWAYS true.

    It is easy to visualize in the two dimensional case. As you know, a linear equation in two unknowns can be graphed as a straight line on a Cartesian plane. If you have two such equations, their simultaneous solution is where their two lines intersect. Right? This is basic stuff. However, if the lines are parallel, the two lines never intersect, which means that their is no simultaneous solution. If the two equations are represented by the SAME line, the "two" lines intersect everywhere, which means that every point on the line is a simultaneous solution.

    If you follow that, then how to solve the problem becomes this: for what values of t are the lines representing the equations parallel and so intersect nowhere, for what values of t are the two lines identical and so "intersect" everywhere, and for what values of t are the two lines distinct but not parallel and so intersect at a single point.

    Show us far you can get with that set of starting hints.
    Thanks from topsquark
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