Question

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

Answer 1

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.

Answer 2

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

Answer 3

I thought B.

Answer 4

It is B, here are all the test answers:
D
C
D
B
100% trust me

Answer 5

@trust me i wont lie
is correct

Answer 6

Trust we I won't lie is correct

Answer 7

@Trust me i wont lie is correct, 100% for connexus algebra 1a unit 7 lesson 1 quick check.