math help please
posted by Deborah .
Which cannot describe a system of linear equations?
exactly two 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
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.
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
I thought B.