math help please

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Which cannot describe a system of linear equations?
no solution
exactly two solutions
infinite solutions
exactly one solution

I thought it was A or D but someone else is telling me it is I'm confused...I thought it was 2 or more solutions

  • math help please -

    If we denote the system of linear equations in matrix form as:

    L y = x (1)

    where y = (y1,y2,y3,...) are the variables you want to solve for, then L being a linear operator, you have that:

    L (a y+ bz) = a L y + b Lz

    So, if y and z are two different solutions to (1), you have:

    L (ay + bz) = (a + b) x


    L[(ay+ bz)/(a+b)] = x

    So, given two different solutions y and z, you can construct an infinite number of others by taking arbitrary linear combinations of the two.

  • math help please -

    A system of linear equations is represented by 2 straight lines

    These two lines can
    1. intersect at one point ---> one solution
    2. be 2 distinct lines parallel to each other ---> no intersection
    3. be the same line ----> infinite number of solutions

    But two straight lines could not possibly intersect at 2 points, so your correct choice is C

  • math help please -

    I thought B.

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