Respuesta :

nobrains
First let's put both into equivalent forms by solving the second equation for y.
8x - 4y = 12
-4y = -8y + 12
y = 2y -3

We now have two equations:
y = mx - 6
y = 2x - 3

Recall that parallel lines have the same slope, and the slope is "m" for an equation in slope-intercept form y=mx+b.
The slope in y = 2x - 3 is 2, so for the equation y = mx -6 to be parallel, it must also have a slope of 2.
Therefore, m = 2.

The value of [tex]m[/tex] is [tex]2[/tex].

Given:

The given equations are:

[tex]y=mx-6[/tex]        ...(i)

[tex]8x-4y=12[/tex]         ...(ii)

To find:

The value of [tex]m[/tex] that will create a system of parallel lines with no solution.

Explanation:

The slope-intercept form of a line is:

[tex]y=mx+b[/tex]           ...(iii)

where, [tex]m[/tex] is the slope and [tex]b[/tex] is the [tex]y[/tex]-intercept.

The slope of line (i) is [tex]m[/tex].

Equation (ii) can be rewritten as:

[tex]-4y=-8x+12[/tex]

[tex]y=\dfrac{-8x+12}{-4}[/tex]

[tex]y=2x-3[/tex]

The slope of this line is [tex]2[/tex].

We know that the slopes of parallel lines are equal. So, [tex]m=2[/tex].

Learn more:

https://brainly.com/question/14874024

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