Question

What is C would mean that the system of equation 2x-3y=1 and cx-3y=2 would not have any solutions

Answer 1

if both coefficients were the same the lines would be parallel

Answer 2

I don't know what that means

Answer 3

i mean if you have
\[2x-3y=1\] and
\[2x-3y=2\] then the lines are parallel

Answer 4

Then had did you know the c was 2

Answer 5

i am not sure what you are asking

Answer 6

Well the second equation had cx but then you substituted it as a 2

Answer 7

Had did you know that

Answer 8

Let me try to explain....when lines have the same slope but different y intercepts, then they are parallel lines and will have no solutions.

2x - 3y = 1 (put this in y = mx + b form where the number in the m position is the slope and the number in the b position is the y intercept)
-3y = -2x + 1 -- divide by -3
y = (-2/-3) x + 1/3
y = 2/3x + 1/3
so our slope here is 2/3 and our y intercept is 1/3

cx - 3y = 2
-3y = -cx + 2 -- divide by -3
y = (-c/-3) - 2/3
y = c/3 - 2/3

now we have to have the same slope in order for them to be parallel. So c will have to be 2 because the slope of the first line was 2/3. And since the y intercepts are both different....that makes the lines parallel, thus, they have no solution

Answer 9

The answer would be 2 even if there is no solution

Answer 10

if c = 2, then the lines are parallel and have no solution.
However, if c would have been a different number, such as 4, then the lines would not be parallel because parallel lines have the same slope, thus, there would be 1 solution.

Learn this...it will help

if the slopes and the y intercepts are the same, then the lines coincide (they lay on top of each other) and they will have infinite solutions.

if the slopes are the same, but the y intercepts are different, then the lines are parallel and they never intersect, thus, they have no solution.

if the slopes and the y intercepts are different, then the lines will intersect, thus having 1 solution.

Answer 11

Oh ok now I get it