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
a.2
b.3
c.1
d.0

Question

imtiaz7 · Answer

is your question is complete?

mathstudent55 · Answer

2x - 3y = 1
cx - 3y = 2

Let's take a look at an equation of the form ax + by = c, and see where the slope comes from.

Solve for y:

$ax + by = c$

$by = -ax + c$

$y = -\dfrac{a}{b}x + \dfrac{c}{b} $

Do you follow this so far?

mathstudent55 · Answer

Since the slope (in the slope-intercept form, or y = mx + b) form is m, our slope is:

$m = -\dfrac{b}{a} $

mathstudent55 · Answer

As you can see, the slope depends only on a and b, the coefficients of x, and y, respectively.

For the system 
2x - 3y = 1 
cx - 3y = 2
not to have a solution, what must the lines be?

anonymous · Answer

@mathstudent55 Thank you !!!

mathstudent55 · Answer

What kind of lines have no solution as a system of equations because they never intersect?

anonymous · Answer

@mathstudent55 parallel ?

mathstudent55 · Answer

Correct.
We want the two lines of the given equations to be parallel.
What do you know about the slopes of parallel lines?

anonymous · Answer

@mathstudent55 they have the same slope

imtiaz7 · Answer

yes you are right @kimm210

mathstudent55 · Answer

Correct.
Parallel lines have the same slope.

Now we know this:
Parallel lines have the same slope.
The slope of a line depends only on the coefficients of x and y in the equation
  ax + by = c

Since we want the equations to be parallel and have the same slope, that means the coefficients of x and y must be in the same ratio.

mathstudent55 · Answer

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