Question

PLEASE HELP!!!! Which of the following values for c would mean that the system of equations 2x − 3y = 1 and cx − 3y = 2 would not have any solutions?

Answer 1

A system of equations that does not have any solutions is one where the lines are parallel. When you compare the lines in y = mx + b form, the m position is the slope and the b position is the y intercept. The lines will be parallel if the slopes are the same and the y intercepts are different.
So lets compare...
2x - 3y = 1 (we will put this in y = mx + b form.....subtract 2x from both sides)
-3y = -2x + 1 (now divide both sides by -3)
y = (2/3)x - 1/3

so the slope is 2/3, and the y intercept is -1/3

now we have :
cx - 3y = 2 (put it in y = mx + b form)
-3y = -cx + 2 (divide by -3)
y = (-c/-3)x - 2/3

now our slopes have to be the same....but the y intercepts cannot.
So that means that the c stands for 2.

Answer 2

2x - 3y = 1 and 2x - 3y = 2 are parallel lines and will have no solution because they will never intersect

Answer 3

Can you show me how they don't intersect

Answer 4

The answers choices are 3, 2, 1, and 0

Answer 5

the c stands for 2.

and if you were to graph :
2x - 3y = 1 and 2x - 3y = 2, you would see that they do not intersect, therefore, no solution.