Posted by **Deborah** on Friday, November 23, 2012 at 10:06pm.

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 B...no I'm confused...I thought it was 2 or more solutions

- math help please -
**Count Iblis**, Friday, November 23, 2012 at 10:59pm
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

Therefore:

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 -
**Reiny**, Friday, November 23, 2012 at 11:15pm
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 -
**Tiff**, Saturday, November 24, 2012 at 12:21am
I thought B.

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