Question

Which value of m will create a system of parallel lines with no solution?

y=mx−6
8x−4y=12

a) 5
b) 3
c) -2
d) -3

Answer 1

The value of m that will create a system of parallel lines with no solution, between the equations y=mx-6 and 8x-4y=12, is m=3. This is because both lines would have the same slope, hence they would never intersect and no solution would exist.

Step-by-step explanation:

To determine which value of m will create a system of parallel lines with no solution for the equations y=mx-6 and 8x-4y=12, we need to rearrange the second equation into slope-intercept form (y=mx+b). Dividing the second equation by -4 we get y=2x-3. For lines to be parallel, their slopes must be equal, and they must have different y-intercepts, meaning no points of intersection. Therefore, we compare the slope of y=2x-3 with the given options.

Option A) 5 would not create parallel lines since the slope would be different.
Option B) 3 is the correct answer because it matches the slope of the second line, creating parallel lines.
Option C) -2 would create lines with different slopes, potentially intersecting.
Option D) -3 gives a different slope, also potentially intersecting.